more fun with similar triangles

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Presentation transcript:

more fun with similar triangles Pamela Leutwyler

AB is parallel to CD B A D C

AB is parallel to CD B  ABC =  BCD A D C

AB is parallel to CD B  ABC =  BCD  ABC =  BCD A  AEB =  CED E D C

AB is parallel to CD B  ABC =  BCD  ABC =  BCD A  AEB =  CED E  BAE =  EDC D ABE is SIMILAR to CED C

AB is parallel to CD B  ABC =  BCD  ABC =  BCD A  AEB =  CED x E  BAE =  EDC X D ABE is SIMILAR to CED C

AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A  AEB =  CED x E  BAE =  EDC X D Y ABE is SIMILAR to CED C

AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A z  AEB =  CED x E  BAE =  EDC X Z D Y ABE is SIMILAR to CED C

X Y Z x y z AB is parallel to CD B  ABC =  BCD  ABC =  BCD y A z  AEB =  CED x E  BAE =  EDC X Z D Y X x Y y Z z = = C

example 1

these lines are parallel

10 feet 9 feet 7 feet x y 3 feet

10 feet 9 feet 7 feet x y 3 feet

10 feet 9 feet 7 feet x y 3 feet

10 feet 9 feet 7 feet x y 3 feet

10 feet 9 feet 7 feet x y = 2.7 3 feet 9 y 10 3 = y = 2.7 feet

10 feet 9 feet 7 feet x= 2.1 y = 2.7 3 feet 7 x 10 3 = x = 2.1

10 feet 9 feet 7 feet x= 2.1 y = 2.7 3 feet

these lines are parallel

these lines are parallel these angles have equal measure

these lines are parallel these angles have equal measure these angles have equal measure

these triangles are similar these lines are parallel these angles have equal measure these angles have equal measure these triangles are similar

R Q P Q P r q p R these triangles are similar = = q p these lines are parallel these angles have equal measure these angles have equal measure r these triangles are similar

example 2

BE is parallel to CD CD = 12 feet BE = 9 feet AD = 20 feet AE = ? C B A D E

12 20 9 x BE is parallel to CD = CD = 12 feet BE = 9 feet AD = 20 feet AE = 15 feet 12 9 20 x = C B A D E x = 15