Geometry: Congruent and Similar Triangles Study

Do the triangles have the same shape? F C 60º 60º 24 cm 16 cm 14 cm 21 cm 40º 80º A B 80º 10 cm 40º D E 15 cm What do you notice about the lengths of the sides? The sides are in the same ratio.

A Construct DABC ÐB = 50º ÐC = 60º 60º 50º BC = 4 cm C B 4 cm P Construct DPQR ÐQ = 50º 4 cm ÐR = 60º PQ = 4 cm 50º 60º R Q Are they identical? No

Congruent Triangles: A X a a c c b b Z C B Y DABC @DXYZ ÐA = Ð AB = ÐB = Ð AC = ÐC = Ð BC =

Conditions for congruence A X 1) B C Y Z A X 2) b b B C Y Z A X 3) c c b b B C Y Z

Similar Triangles X A a DABC ~ DXYZ a c c b b B C Y Z All angles are equal Sides are proportional

X Conditions for similarity A 1) B C Y Z X A 2) b b B C Y Z X A 3) c c b b B C Y Z

Example: If DPQR ~ DSTU then ÐS ÐP = ÐT ÐQ = ÐU ÐR = Example: Show that DDEF ~ DXYZ D What is the scale factor? 4 2 X 6 F E 3 the scale factor is Z Y

Example: Show that DDEF ~ DXYZ D ÐD = Ð ÐE = Ð ÐF = Ð X 30° 90° 60° F E 90° Z Y \DDEF ~ D

Example: Show that DABC ~ DPQR P A 4 6 3 2 B C 5 Q R 7.5 \DABC ~ DPQR What is the scale factor?

Are the triangles similar?

Are the triangles similar? 4 6 3 4.5

Calculate the values of x and y. 15 12 x 14 8 y

A tree is 3 m tall and casts a shadow of 2 m. A building casts a shadow of 12 m. Determine the height of the building. x 3 m 2 m 12 m The building is x =

Geometry: Congruent and Similar Triangles Study