Top Banner
Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar
13

Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Jan 03, 2016

Download

Documents

Kelly Wade
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Objective:After studying this section, you will be able to use several methods to prove triangles are similar.

8.3 Methods of Proving Triangles Similar

Page 2: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Postulate If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the three angles of another triangle, then the triangles are similar. (AAA)

Page 3: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Theorem If there exists a correspondence between the vertices of two triangles such that the two angles of one triangle are congruent to the two corresponding angles of other, then the triangles are similar. (AA)

Page 4: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given:

Prove:

A

B C

D

E F

EB

DA

~ ABC DEF

Page 5: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Theorem If there exists a correspondence between the vertices of two triangles such that the ratios of themeasures of corresponding sides are equal, then the triangles are similar. (SSS similarity)

Page 6: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given:

Prove:

A

B C

D

E F

DF

AC

EF

BC

DE

AB

~ ABC DEF

Page 7: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Theorem If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of two pairs ofcorresponding sides are equal and the included angles are congruent, then the triangles are similar. (SAS Similarity)

Page 8: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given:

Prove:

A

B C

D

E FEBEF

BC

DE

AB

~ ABC DEF

Page 9: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given: parallelogram YSTW

Prove:

D

BA

C

F

E

~ BFE CFD

Page 10: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given:

Prove: ~ PEN PAL

EARP

N

EALP

trisect and

LP ofmidpoint theis

E P R A

L

N

Page 11: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Given:

Prove: ~ KHJ HGJ

GHJright of GJ hypotenuse

toaltitude theis

KH

G

J

H

K

Page 12: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

The sides of one triangle are 8, 14, and 12, and the sides of another triangle are 18, 21, and 12. Prove that the triangles are similar.

Page 13: Objective: After studying this section, you will be able to use several methods to prove triangles are similar. 8.3 Methods of Proving Triangles Similar.

Summary: If you were to draw a triangle and have a line parallel to the base,creating two triangles, would the triangles be similar if you had a right triangle? Obtuse? Acute? Why?

Homework: worksheet