Angle Relationships, Similarity and Parallelograms

 Point  Line  Plane

 Lines that intersect to form right angles. What is the symbol for perpendicular? It looks like “  ”.

 Review your worksheets.  What does a midpoint of a segment do?  It makes two congruent segments.  What does a bisector of an angle do?  It makes two congruent angles.

 It means objects are the same shape and size.  Set them equal.

 Vertical angles  Linear Pair  Complementary angles  Supplementary angles

 Vertical angles are congruent  …looks like a bow tie

 Linear pair angles have a sum of 180°

 Complementary angles have a sum of 90°.  Supplementary angles have a sum of 180°.

 If the lines are parallel, then alternate interior angles are congruent. (Look for Z)  If the lines are parallel, then corresponding angles are congruent. (Look for F)  If the lines are parallel, then consecutive interior angles are supplementary. (C – supp)

 Polygons whose corresponding side lengths are proportional and corresponding angles are congruent.

 Ratio of the lengths of two corresponding sides (always reduce)

 If two polygons are similar then the ratio of their perimeters is equal to the ratios of the corresponding side lengths.

 AA~  SAS~  SSS~

 If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

 If an angle of one triangle is congruent to an angle of another triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

 If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

 One pyramid has a height of 9 feet and the other has a height of 12 feet. If the two pyramids are similar, then  What is the scale factor of the smaller to the larger?  Answer: 3:4  What is the scale factor of the area of their bases?  Answer: 9:16  The volume of the smaller is 28 meters cubed. What is the volume of the larger?  Answer: meters cubed

 If a triangle has two congruent sides, then the angles opposite those sides are congruent.  Or Base angles of an isosceles triangle are congruent.

 It is a quadrilateral with two pair of opposite sides parallel.

 Opposite sides are parallel.  Opposite sides are congruent.  Opposite angles are congruent.  Consecutive angles are supplementary.  Diagonals bisect each other.

 A quadrilateral with four right angles. What is another property of a rectangle? Answer: The diagonals are congruent.

 A quadrilateral with four congruent sides. What is a special property of a rhombus? Diagonals are perpendicular.

 A median is a segment from a vertex of a triangle to the midpoint of the opposite side.

 At a point called the centroid

 From the vertex to the centroid of the triangle is 2/3 the length of the median.

 The segment that joins the midpoints of two sides of a triangle is parallel to the third side and is ½ the length of the third side. What does x equal? 3

 The length of the segment that joins the midpoints of the legs of a trapezoid is ½ the length of the sum of the bases.