7-5: Parts of Similar Triangles Expectations: G1.2.5: Solve multi-step problems and proofs about the properties of medians, altitudes and perpendicular bisectors to the sides of a triangle and the angle bisectors of a triangle. G2.3.4: Use theorems about similar triangles to solve problems with and without the use of coordinates.
Proportional Perimeters Theorem If two triangles are similar, then the ratio of corresponding perimeters is equal to the ratio of corresponding sides.
Proportional Perimeters Theorem If F ~ G, then: F a c b y z x G a b c a + b + c x y z x + y + z =
If ABC ~ XYZ, AB = 15, XY = 25 and the perimeter of XYZ = 45, what is the perimeter of ABC?
Corresponding Altitudes Theorem If two triangles are similar, then the ratio of corresponding altitudes is equal to the ratio of corresponding sides.
Corresponding Altitudes Theorem b z y x w F G If F ~ G, then, a b c d w x y z =
If CDE ~KLM, determine the value of x. 12.5 10 M 16 8 K L
Corresponding Angle Bisectors Theorem If two triangles are similar, then the ratio of corresponding angle bisectors is equal to the ratio of corresponding sides.
Corresponding Angle Bisectors Theorem F G a x w d c b z y If F ~ G, then, a b c d w x y z =
The triangles below are similar and AD and EH are angle bisectors The triangles below are similar and AD and EH are angle bisectors. Determine the perimeter of ∆EHG. E F G H 10.4 x 8 A B C D 13 9 7
Corresponding Medians Theorem If two triangles are similar, then the ratio of corresponding medians is equal to the ratio of corresponding sides.
Corresponding Medians Theorem F G a x d c b z y w If F ~ G, then, a b c d w x y z =
∆ABC ~ ∆XYZ. If the perimeter of ∆XYZ is half as much as the perimeter of ∆ABC, and AD and XU are medians, determine the length of XU. X A 22 Z U Y C D B
Angle Bisector Theorem An angle bisector of a triangle separates the opposite side into segments that have the same ratio as the other two sides.
Angle Bisector Theorem D C B If CD bisects ACB then, AC BC . AD BD =
Determine the value of x in the figure below. C B 24 x 14 12
Assignment pages 373 – 377, # 13 – 33 (odds), 43, 47-57 (all).