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Analytic Geometry EOCT Review
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Proofs Which item can be given as a statement in a proof?
A. Given B. Def. of congruent segments C. m<1 + m< 2= 180 D. Trans. Prop. of Equality
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Proofs Identify the property that justifies the statement.
m = n, so n = m KL = KL p = q and q = -1, so p = -1
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Proofs Algebraic Proof
Solve the equation below. Write a justification for each step. 1/5(a + 10) = -3
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Parallelograms Properties of Parallelograms
- Opposite sides are parallel and congruent - Opposite angles are congruent - Consecutive angles are supplementary - Diagonals bisect each other
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Parallelograms WXYZ is a parallelogram. Find the measure of angle W.
Find the value of x.
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Parallelograms In parallelogram JKLM, what is the value of <K?
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Parallelograms ABCD is a parallelogram. Find AB and BX.
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Parallelograms In parallelogram DEFG, what is EG?
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Angles formed by Lines and Transversals
Corresponding Angles are congruent Alternate Interior Angles are congruent Alternate Exterior Angles are congruent Same Side Interior Angles are supplementary
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Angles formed by Lines and Transversals
Find each angle measure.
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Angles formed by Lines and Transversals
Find x.
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Congruence 5 Triangle Congruence Theorems Side-Side-Side
Side-Angle-Side Angle-Angle-Side Angle-Side-Angle Hypotenuse Leg (right triangles only) Angle-Side-Side is NOT a theorem
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Congruence If ΔKLM ≅ ΔRST, find the value of x.
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Congruence What is the measure of angle U?
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Congruence ΔJKL≅ ΔMNP. KL = 21x - 2, NP = 20x, LJ = 15x and PM = 13x Find LJ.
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Congruence
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Similarity 3 Triangle Similarity Theorems Side-Side-Side
Side-Angle-Side Angle-Angle
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Similarity What theorem proves the triangles are similar?
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Similarity What theorem proves the triangles are similar?
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Similarity What is the length of AC?
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Similarity Find SP.
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Similarity
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Similarity
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Similarity A drawing of a garden uses a scale of 1 in : 3 ft. Find the length of the garden if the length on the drawing is 13 inches.
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Exterior Angles Theorem
Find measure of <RST.
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Midsegment Theorem Find QR. What type of segment is QR?
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Midsegment Theorem
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Triangles What is the length of the longest side of the triangle?
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Angle relationships in Triangles
What is the value of x if the acute angles of a right triangle measure 8x° and 12x°? The angles of a triangle measure 4°, 86°, and 90°. Which classification of the triangle is correct? One angle of an equilateral triangle measures (4x - 20). What is the value of x?
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Special Right Triangles
There are 2 types of special right triangles: In a triangle, the legs have equal length and the hypotenuse is the length of one of the legs multiplied by √2. In a triangle, the hypotenuse is the length of the shorter leg multiplied by 2, and the longer leg is the length of the shorter leg multiplied by √3.
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Special Right Triangles
Find the value of x.
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Special Right Triangles
Find the value of x.
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Trigonometry SOHCAHTOA Sin = opp/hyp Cos = adj/hyp Tan = opp/adj
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Trigonometry 1. Find tan K. 2. Find cos M. 3. Find sin K.
4. To the nearest degree, what is the measure of <M?
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Trigonometry A 24-foot ladder forms a 76° angle with the ground. The top of the ladder rests against a building. To the nearest inch, how high up the building does the ladder reach? One acute angle of a right triangle measures 28°. To the nearest tenth, what is the length of the side opposite that angle if the hypotenuse measures 16 meters? A skateboard ramp makes a 22° angle with the ground. To the nearest foot, how high is the ramp?
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Trigonometry 1. Find sin (1.54).
2. If sin A = 8/17, find the measure of angle A.
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Trigonometry Use the figure below to find each of the following:
1. m<A. 2. length of AB 3. m<B.
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Lines that Intersect Circles
Use the figure below to find each of the following: Chord Secant Tangent Diameter Radius
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Lines that Intersect Circles
To the nearest tenth, what is the length of MN?
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Central and Inscribed Angles
A central angle is EQUAL to the measure of its intercepted arc. An inscribed angle is HALF the measure of its intercepted arc. An angle inscribed in a semicircle is ALWAYS a right angle. If two inscribed angles intercept the same arc, the angles are congruent.
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Central and Inscribed Angles
Find the measure of arc JK. Then, find the measure of arc JIL.
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Central and Inscribed Angles
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Central and Inscribed Angles
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Central and Inscribed Angles
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Central and Inscribed Angles
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Inscribed Quadrilaterals
Opposite angles in an inscribed quadrilateral are supplementary.
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Arc Length Find the measures of arcs MN and XY.
Formula is not on the sheet
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Sector Area Find the areas of sectors BAC and QPR.
Formula is not on the sheet
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Spheres Volume and Surface Area formulas are on the sheet
Find the volume and surface area of the sphere.
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Spheres Find the surface area of a sphere with a volume of 256Π cm3
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Volume All formulas are on the sheet
Find the volume of each figure below.
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Volume Find the volume of the cylinder.
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Volume Find the volume of each pyramid.
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Volume Find the volume of the cone.
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Volume Find the volume of the composite figures.
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