Prove Given: ∥, and are transversals Prove: ∠2 is supplementary to ∠8 1 2 3 4 5 6 7 8
Similar Shapes
• Two shapes are similar when one can become the other after a resize, flip, slide or turn.
• The symbol ~ means “similar to”
Properties:
• Corresponding angles are congruent
• Corresponding side measurements are proportional
Similar ShapesProperties:
• Corresponding angles are congruent
• Corresponding side measurements are proportional
• GIVEN: ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
Corresponding parts of similar figures
• GIVEN: The triangles are similar.
• ∠A corresponds with ∠____.
• ∠B corresponds with ∠____.
• ∠C corresponds with ∠____.
• AB matches with ______.
• XZ matches with ______.
• BC matches with ______.
A
B C
X
Y
Z30°
30°
70°
70°80°
80°
• AB matches with ______.
• ZY matches with ______.
• BC matches with ______.
• GIVEN: ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍
• ∠A corresponds with ∠____.
• ∠B corresponds with ∠____.
• ∠C corresponds with ∠____.
Corresponding parts of similar figures
A
B C
X
Y
Z
Finding side lengths of similar triangles
• Because side lengths are proportional, we can set up a PROPORTION
L
M
N
RS
T
6
12100
x
Angle-Angle Similarity
• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
A
B C
X
Y Z10°10°
55°
55°
Similarity statement:
Applications of similar triangles
A 40-foot flagpole casts a 25-foot shadow. Find the shadow cast by a nearby building 200 feet tall.
40 ft
25 ft
200 ft
x
Applications of similar triangles
A tree 24 feet tall casts a shadow 12 feet long. John is 6 feet tall. How long is John's shadow? (Draw a diagram and solve)
Applications of similar triangles
A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower? (Draw a diagram and solve)
Applications of similar triangles
A cell phone tower casts a 100-foot shadow. At the same time, a 4-foot 6-inch post near the tower casts a shadow of 3 feet 4 inches. Find the height of the tower.