Geometry Warm-Up 1/19/11

15105

4510

8

A

B

C

D

F

E

1. Find the scale factor.

2. Find the length of DE.

3. Find the measure of E.

∆ABC ~ ∆EDF

Section 7.3 Similar Triangles

Geometry

January 19, 2011

Similar Polygons

Polygons are similar if:1) The corresponding angles are congruent

2) The sides are proportional

Ex 1: In the diagram, ∆BAD ~ ∆EAC.

Write the statement of proportionality.

Find the m∠AEC.

Find EA & BE.

20

34

79

12

3

A

B D

E C

Ex 2: In the diagram, ∆ LMN ~ ∆ PQN.

Write the statement of proportionality.

Find the m∠ M &

m∠ P.

Find MN & QM.30

33

20

36

106N

L M

PQ

Angle-Angle Similarity Postulate

AA ~ – Two triangles are considered similar if 2

angles in one triangle are to 2 angles in another triangle.

K

L

M

A

B

C

Side-Side-Side Similarity Postulate Side-Side-Side

(SSS)- when the corresponding sides of two triangles are proportional – AB = BC = CA

PQ QR RP

A

B C

P

Q R

Side-Angle-Side Similarity Postulate Side-Angle-Side

(SAS)- when an angle in one triangle is congruent to an angle in a second triangle and the lengths of the included sides are proportional X=M and ZX = XY

PM MN

X

ZY

M

PN

Which of the following triangles are similar?

96

12G H

I

106

14A C

B4

8

6

J

L K

Ex 3: Low-level aerial photos can be taken using a remote-controlled camera suspended from a blimp. You want to take an aerial photo that covers a ground distance g of 50 meters. Use the proportion f/h = n/g to estimate the altitude h that the blimp should fly at to take the photo. In the proportion use f=8cm and n=3cm. These two variables are determined by the type of camera used.

Ex 4: Find the length of the altitude QS.

88

6

1212

Q

N P

TRS

M

HOMEWORK:

P. 401 (7-15)

Geometry 1/20/11

Choose one problem from the homework for your group to present. Once you have selected the problem, write the number on the board with the name of someone from your group!