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