Transcript sides and angles are congruent

Extension 3.6 Proportions and Similar Figures
A. What do you know about similar triangles and congruent triangles?
B. Definitions
1. Similar triangles – have the same shape, but not necessarily the same size
Symbol: ~ similar
characteristics: angles are congruent
sides are in proportion
2. Congruent triangles – have the same shape and size
Symbol:  congruent
characteristics: sides and angles are congruent
C. Name the corresponding sides and angles. Then, solve for x if ABC ~ DEF .
F
B
15cm
A
21cm
18cm
10cm
C
D
x cm
E
Continued Examples: Given ABCD ~ FGHJ, find AD
C
D
H
J
x
B
40 m
A
14 m
G
35 m
F
Applying Similarity – Indirect Measurement
1.) A tree cast a shadow 7.5 ft long. A girl 5 ft tall casts a shadow 3 ft long. The triangle
shown for the tree and its shadow is similar to the triangle shown for the woman and her
shadow. How tall is the tree?
Review of Scale Drawing
1.) Scale Drawing – an enlarged or reduced drawing that is similar to an actual object
or place.
2.) Scale – ratio of a distance in the drawing to the corresponding actual distance.
Examples:
1.) The scale of the map of Pennsylvania says that 1 inch: 10miles. Approximately
how far is it from York to Philadelphia if the map distance is 12.5 in. ?
2.) A blueprint for a house states that 2.5 inches equals 12 feet. If the length of a
wall is 16feet, how long is the wall in the blueprint?
3.) A collector’s model racecar is scaled so that 1 inch on the model equals 6.25 feet
on the actual car. If the model is 2/3 inch high, how high is the actual car?