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Acute Angle An angle whose measure is less than 90°

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Presentation on theme: "Acute Angle An angle whose measure is less than 90°"— Presentation transcript:

1 Acute Angle An angle whose measure is less than 90°

2 Adjacent Angles Two angles with a common vertex and a common side.

3 Alternate Exterior Angles
2 and 8 1 and 7 Two non-adjacent angles that lie on the opposite sides of a transversal outside two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

4 Alternate Interior Angles
3 and 6 4 and 5 Two non-adjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

5 Angle Formed by 2 rays (sides) with the same endpoint (vertex). X 3 V
Z 3

6 Angle Addition Postulate
If T is in the interior of ∠QRS, then m∠QRT + m∠TRS = m∠QRS.

7 Angle Bisector A ray that divides an angle into two congruent angles.

8 Auxiliary Line A line (or ray or segment) added to a diagram to help in a proof or in determining the solution to a problem. DE is an auxiliary line.

9 Biconditional Two statements connected by the words “if and only if.”

10 Collinear Points that are on the same line. A B C D E
A, B, C, and D are collinear points. A, B, C, D, and E are non-collinear points.

11 Complementary Two angles whose measures have a sum of 90.

12 Compound Statement A statement formed when two or more simple statements are connected as either a conditional (if-then), a biconditional (if and only if), a conjunction (and), or a disjunction (or).

13 Conclusion The “then” statement in an if-then statement.

14 Conditional Statement
A statement that tells if one thing happens another will follow. Example: “If a polygon has three sides then it is a triangle.”

15 Congruent Exactly equal in size and shape.
Congruent segments have the same length. Congruent angles have the same measure.

16 Congruent Angles Angles that have the same measure. W X

17 Congruent Segments Segments that have the same length. J K L M

18 Conjecture An educated guess, opinion, hypothesis.

19 Conjunction Two statements joined by the word and, represented by the symbol ^.

20 Contrapositive A version of a conditional statement formed by interchanging and negating both the hypothesis and conclusion of the statement.

21 Converse A version of a conditional statement formed by interchanging the hypothesis and conclusion of the statement.

22 Coplanar Lines Lines that are in the same plane.

23 Coplanar Points Points that are in the same plane. F A B E C D
A, B, C, D, and E are coplanar points. A, B, C, D, E, and F are non-coplanar points.

24 Corresponding Angles 1 and 5 2 and 4 3 and 8 4 and 7
Two non-adjacent angles that lie on the same side of a transversal, in “corresponding” positions with respect to the two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

25 Counterexample An example that shows that a conjecture is not always true.

26 Deductive Reasoning The use of facts, definitions, rules and/or properties to prove that a conjecture is true.

27 Disjunction The symbol v represents a disjunction, you read it as “or.”

28 Distance Formula The distance between 𝑥 1, 𝑦 1 and 𝑥 2 , 𝑦 2 can be found using the formula 𝑥 2 − 𝑥 ( 𝑦 2 − 𝑦 1 ) 2

29 Endpoint A point at one end of a segment or the starting point of a ray.

30 Hypothesis The “if” clause in an if-then statement.

31 Inductive Reasoning The process of observing data, recognizing patterns, and making a generalization.

32 Inverse A version of a conditional statement formed by negating both the hypothesis and conclusion of the statement.

33 Line A set of points that extends in 2 directions without end. m A B
Line m or line AB or AB

34 Segment MN or Segment NM or MN or NM
Line Segment Part of a line consisting of two endpoints and all points between them. N M Segment MN or Segment NM or MN or NM

35 Linear Pair A pair of adjacent angles whose noncommon side are opposite rays.

36 Logically Equivalent When two statements have the same exact truth values.

37 Midpoint A point that divides a segment into two congruent segments. A
B

38 Midpoint Formula The midpoint of a segement with endpoints 𝑥 1, 𝑦 1 and 𝑥 2 , 𝑦 2 can be found using the formula 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2

39 Negation of p The symbol ~p is the negation of p and can be read as “not p.”

40 Obtuse Angle An angle whose measure is greater than 90° but less than 180°.

41 Opposite Rays Two collinear rays with the same endpoint. They always form a line. F H D HF and HD are opposite rays.

42 Parallel Lines Coplanar lines that do not intersect. a c a//c

43 Parallel Planes Planes that do not intersect. W M

44 Perpendicular Lines 2 lines intersect to form right angles. A C B

45 Perpendicular Planes Planes intersect to form right angles. B D

46 Plane A flat surface that extends in all directions without end. It has no thickness. W A B C Plane W or Plane ABC

47 Point A location in space •A

48 Postulate A statement that is accepted without proof.

49 Proof An argument that transforms a conjecture to a theorem through the application of logical reasoning or deductive reasoning.

50 Pythagorean Theorem For sides a, b, and c in a right triangle, a2 + b2 = c2.

51 Pythagorean Triple Three integers a, b, and c such that a2 + b2 = c2

52 Ray Part of a line consisting of one endpoint and all points of the line on one side of the endpoint. R S RS not SR

53 Right Angle An angle whose measure is exactly 90°.

54 Same Side Exterior Angles
1 and 8 2 and 7 Two angles that lie on the same side of a transversal and outside the lines cut by the transversal. If the lines are parallel, then the angles are supplementary.

55 Same Side Interior Angles
3 and 5 4 and 6 Two angles that lie on the same side of a transversal and between the lines cut by the transversal. If the lines are parallel, then the angles are supplementary.

56 Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.

57 Segment Bisector A line, segment or ray that intersects a segment at its midpoint A C B

58 Slope The ratio of the vertical change of a line to the horizontal change of the line.

59 Slope-Intercept Form A line with a slope m and y-intercept b can be written in the form y = mx + b.

60 Straight Angle An angle whose measure is exactly 180°.

61 Supplementary Two angles whose measures have a sum of 180.

62 Tautology A statement that is always true.

63 Theorem A result that has been proved to be true (using facts that were already known).

64 Transversal A line that intersects two or more coplanar lines at different points. Transversal

65 Truth Table Truth tables are used to determine the conditions under which a statement is true or false.

66 Truth Value The truth value of a statement is the truth or falsity of that statement.

67 Vertex The common endpoint of the sides of the angle. Vertex

68 Vertical Angles The non-adjacent angles formed by two intersecting lines.

69 y-Intercept The y coordinate of the point where a graph intersects the y-axis.

70 AcuteTriangle A triangle with three acute angles.

71 Altitude of a Triangle A segment from a vertex and perpendicular to the opposite side or the line containing the opposite side.

72 Angle-Angle-Side (AAS)
If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. ∠𝐵≅∠𝐸, ∠𝐶≅∠𝐹,𝐴𝐶≅𝐷𝐹,so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

73 Angle-Side-Angle (ASA)
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. ∠𝐵≅∠𝐸,𝐵𝐶≅𝐸𝐹, ∠𝐶≅∠𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

74 Apothem The perpendicular segment from the center of a regular polygon to the midpoint of a side.

75 Base Angles The two congruent angles in an isosceles triangle.

76 Bases (of a trapezoid) The parallel sides of a trapezoid.

77 Centroid The point where the medians of a triangle intersect.

78 Circumcenter The point where the three perpendicular bisectors of a triangle intersect. Circumcenter

79 Circumscribe To draw on the outside of, touching as many points as possible.

80 Circumscribed Circle A circle that contains all the vertices of a polygon.

81 Concave Polygon A polygon that has one or more interior angles that are greater than 180˚.

82 Congruent Triangle Two or more triangles whose side lengths and angle measures are congruent.

83 Convex Polygon A polygon in which all interior angles have measures less than 180˚.

84 Corresponding Parts The angles, sides and vertices that are in the same location in congruent or similar figures.

85 Diagonal A segment that connects two non-consecutive vertices of a polygon. Diagonal

86 Equiangular A geometric figure in which all angles are equal.

87 Equilangular Triangle
A triangle with three congruent angles.

88 Equilateral A geometric figure in which all sides are equal.

89 Equilateral Triangle A triangle with three congruent sides.

90 Exterior Angle The angle formed by extending a side of a polygon.

91 Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and then the larger third side is across from the larger included angle.

92 Hypotenuse-Leg (HL) If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent. 𝐴𝐶≅𝑍𝑌, 𝐴𝐵≅𝑍𝑋 so ∆𝐴𝐵𝐶 ≅∆𝑍𝑋𝑌

93 Incenter The point of concurrency of the angle bisectors of a triangle. Incenter

94 Interior Angle An angle inside a shape.

95 Isosceles Trapezoid A trapezoid with congruent legs.

96 Isosceles Triangle A triangle with two or more congruent sides and angles.

97 Kite A quadrilateral who two distinct pairs of adjacent congruent sides.

98 Legs (of a trapezoid) The nonparallel sides of a trapezoid.

99 Median of a Triangle A segment from a vertex to the midpoint of the opposite side.

100 Midsegment The segments whose endpoints are the midpoint of two sides of a triangle.

101 Obtuse Triangle A triangle with one obtuse angle.

102 Orthocenter The point where the three altitudes of a triangle intersect. Orthocenter

103 Parallelogram A quadrilateral in which both pairs of opposite sides are parallel and congruent. Opposite Angles are congruent and consecutive angles are supplementary.

104 Perpendicular Bisector of a Triangle
A line or segment that is perpendicular to the side of a triangle at its midpoint. Perpendicular Bisector

105 Point of Concurrency The point where three or more lines intersect.

106 Polygon A closed plane figure formed by segments that only intersect at their endpoints.

107 Quadrilateral A polygon with four sides.

108 Rectangle A parallelogram with four right angles and congruent diagonals.

109 Regular Polygon A polygon that is both equilateral and equiangular.

110 Remote Interior Angles
An interior angle in a polygon that is not adjacent to the exterior angle. In a triangle the sum of the two remote interior angles is equal to the exterior angle.

111 Rhombus A parallelogram with all sides congruent and diagonals that are perpendicular

112 Right Triangle A triangle with one right angle and two acute angles.

113 Scalene Triangle A triangle with no congruent sides.

114 Side-Angle-Side (SAS)
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. 𝐴𝐵≅𝐷𝐸,∠𝐵≅∠𝐸, 𝐵𝐶≅𝐸𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

115 Side-Side-Side (SSS) If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent. 𝐴𝐵≅𝐷𝐸, 𝐴𝐶≅𝐷𝐹,𝐵𝐶≅𝐸𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

116 Square A parallelogram with all sides congruent and four right angles.
A square has all the properties of a rectangle and a rhombus.

117 Trapezoid A quadrilateral with exactly one pair of parallel sides.

118 Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

119 Adjacent Leg The leg that is closest to the included angle in a right triangle.

120 Angle-Angle Similarity (AA~)
In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar. ∠𝐴 ≅∠𝑃 and ∠𝐵 ≅∠𝑄 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

121 Angle Bisector Proportionality Theorem
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

122 Constant of Proportionality
The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality

123 Cosecant The cosecant of an acute angle in a right triangle is the ratio of the length of the hypotenuse to the length of the opposite side.

124 Cosine The cosine of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.

125 Cotangent The cotangent of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the opposite side.

126 Geometric Mean

127 Opposite Leg The leg that is across from the included angle in a right triangle.

128 Parallel Proportionality Theorem
If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. 𝑣∥𝑡∥𝑥 so 𝐴𝐵 𝐵𝐶 = 𝐷𝐸 𝐸𝐹 , 𝐴𝐶 𝐴𝐵 = 𝐷𝐹 𝐷𝐸 , 𝐴𝐶 𝐵𝐶 = 𝐷𝐹 𝐸𝐹

129 Secant The secant of an acute angle in a right triangle is the ratio of the length of the hypotenuse to the length of the adjacent side.

130 Side-Angle Side Similarity (SAS~)
If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar. 𝐴𝐶 𝑃𝑅 = 𝐵𝐶 𝑄𝑅 and ∠𝐶≅∠𝑅 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

131 Side-Side-Side Similarity (SSS~)
If the corresponding sides of two triangles are proportional, then the two triangles are similar. 𝐴𝐶 𝑃𝑅 = 𝐵𝐶 𝑄𝑅 = 𝐴𝐵 𝑃𝑄 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

132 Similar Polygon Polygons with congruent corresponding angles and corresponding side lengths in proportion.

133 Sine The sine of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

134 Special Right Triangle
and are called special right triangles because they have some regular feature that makes calculations on the triangle easier.

135 Tangent The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

136 Triangle Proportionality Theorem
If two or more lines parallel to a side of a triangle intersect the other two sides of the triangle, then they divide them proportionally. 𝐴𝐶 𝐶𝐸 = 𝐴𝐵 𝐵𝐷

137 Angles formed by Chords
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. 𝑚∠1=1/2(𝑚 𝑃𝑄 +𝑚 𝑅𝑆)

138 Angles formed by Secants
If two secant segments intersect outside a circle, then the measure of the angle formed is one half the difference of the measure of the intercepted arcs. 𝑚∠𝐸=1/2(𝑚 𝐶𝐷 −𝑚 𝐵𝐴)

139 Angles formed by Tangents
If two tangent segments intersect outside a circle, then the measure of the angle formed is one half the difference of the measure of the intercepted arcs. 𝑚∠𝐶=1/2(𝑚 𝐴𝐸𝐵 −𝑚 𝐵𝐴)

140 Arc A continuous part of a circle. The measure of the arc is the measure of the angle formed by the two radii with endpoints at the endpoints of the arc.

141 Central Angle An angle whose vertex is at the center of a circle and whose sides are radii of the circle Central Angle

142 Chords A line segment on the interior of a circle with both endpoints lying on the circle.

143 Circle The set of all points in a plane that are a given distance (the radius) from a given point (the center) in the plane.

144 Congruent Arc Arcs of a circle that have the same length.

145 Diameter A chord that contains the center of the circle

146 Equation of a Circle The equation of a circle with center (h,k) and radius r is (x – h)2 + (y – k)2 = r2

147 External Secant Segment
The parts of a secant segments that are outside the circle. EF and EH are external secant segments

148 Inscribed Angle An angle whose vertex is on the circle and whose sides are chords of the circle. Inscribed Angle

149 Major Arc An arc with a measure greater than 180˚.

150 Minor Arc An arc with a measure less than 180˚.

151 Point of Tangency The point where the tangent line intersects a circle. A radius is perpendicular the tangent at the point of tangency.

152 Radius A segment from the center of a circle to a point on the circle.

153 Secant Line/Segment A line/segment that intersects a circle exactly twice.

154 Sector A region formed by two radii and an arc of a circle.

155 Segments Lengths in Circles formed by Chords
If two chords of a circle intersect, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. 𝑃𝐴∙𝑃𝐷=𝑃𝐶∙𝑃𝐵

156 Segments Lengths in Circles formed by Secants
If two secants intersect at a point outside a circle, the product of one secant segment and its external secant segment equals the product of the other secant segment and its external secant segment. 𝑃𝐴∙𝑃𝐷=𝑃𝐶∙𝑃𝐵

157 Segments Lengths in Circles formed by a Secant and a Tangent
If a secant and a tangent intersect at a point outside a circle, the product of the length of the secant segment and its external secant segment equals the square of the length of the tangent segment. 𝑃𝐴 2 =𝑃𝐶∙𝑃𝐵

158 Tangent Line/Segment A line or segment that intersects a circle exactly once.

159 Dilation A transformation in which the image is similar (but not congruent) to the pre-image.

160 Reflection A transformation in which a figure is flipped over a line, called a line of reflection.

161 Rotation A transformation in which each point of the pre-image travels clockwise or counterclockwise around a fixed point a certain number of degrees.

162 Tessellation A covering of a plane consisting of one or more types of shapes such that there are no overlaps or gaps between the shapes.

163 Translation A transformation that moves each point of a figure the same distance and in the same direction.

164 Cone A solid bounded by a circular base and a curved surface with one vertex

165 Cross Section The intersection of a solid figure and a plane.

166 Cylinder A solid bounded by two congruent and parallel circular bases joined by a curved surface.

167 Edges The line segment formed by the intersection of two faces of a polyhedron.

168 Faces One of the polygons that make up a three dimensional solid figure.

169 Hemisphere A half-sphere.

170 Isometric Drawing A drawing on isometric dot paper the represents a three-dimensional figure and shows the top, side, and front views.

171 Lateral Area The surface area of a solid excluding the base(s).

172 Lateral Faces The nonparallel bases, or bases, of a solid.

173 Net A two-dimensional drawing used to represent or form a three-dimensional object or solid.

174 Oblique Not perpendicular.

175 Polyhedron A closed three-dimensional figure consisting of polygons that are joined along their edges.

176 Prism A polyhedron that has two congruent parallel faces (bases) that are joined by faces that are parallelograms.

177 Pyramid A polyhedron with three or more triangular faces that meet at a point (vertex) and one other polygonal face called the base.

178 Slant Height It is the shortest distance from the vertex of a cone or pyramid to the edge of the base.

179 Sphere The set of all points (x, y, z) that are a given distance, the radius, from a point, the center.

180 Surface Area The total area of all the surfaces of a three-dimensional figure.

181 Volume The number of cubic units in a three-dimensional figure.


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