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Warm Up

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1. If the volume of sphere is equal to 454 cm³ find the radius

2. The circumference of a circle is 24. Find the area of the circle

Unit 1 Part BReview

Congruent Triangles

Congruent triangles have 3 congruent sides and 3 congruent angles.

The parts of congruent triangles that “match” are called corresponding parts.

Congruence Statement

In a congruence statement

ORDER MATTERS!!!!

Everything matches up.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

B

If ABC DEF,

then BC ___

A

C

D

F

E

If CAT DOG,

then AC ___

BCA ____

____ GFE

- Sides
- Angles

Side-Side-Side (SSS) Congruence Postulate

All Three sides in one triangle are congruent to all three sides in the other triangle

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

(the angle is in between the 2 marked sides)

A

A

A

A

S

S

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

Angle-Side-Angle (ASA) Congruence Postulate

A

A

S

S

A

A

Two angles and the INCLUDED side

(the side is in between the 2 marked angles)

HL

SSS

SAS

ASA

AAS

HL

NO BAD WORDS

The ONLY Ways To Prove Triangles Are Congruent

Share a side

Reason: reflexive property

Vertical Angles

Reason: Vertical Angles are congruent

Proving Triangles

Similar

Angle-Angle (AA~) Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

D

A

E

F

C

B

Side-Angle-Side (SAS~) Similarity THM

If the lengths of two sides are proportional and the included angle is congruent, then the triangles are similar

D

A

F

E

B

C

Side-Side-Side (SSS~) Similarity THM

If the corresponding sides of two triangles are proportional, then the triangles are similar.

D

A

E

F

C

B

Ex. Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement.

Yes, AA~

M

G

68°

43°

68°

43°

H

F

L

K

V

NO

Y

7

3

Z

5

X

W

U

11

1.

3.

2.

Figures that are similar(~) have the same shape but not necessarily the same size.

Have the same size and shape

EXACTALY THE SAME!!!!!

Represented by:

Similar figures have the same shape but not necessarily the same size.

#1 Identify the pairs of congruent angles and corresponding sides

0.5

N Q and P R.

By the Third Angles Theorem, M T.

A similarity ratiois the ratio of the lengths of

the corresponding sides of two similar polygons.

The similarity ratio of ∆ABC to ∆DEF is , or .

The similarity ratio of ∆DEF to ∆ABC is , or 2.

Think: What am I multiplying or dividing all sides by to get the lengths of the other triangle?

Also known as the SCALE FACTOR or DIALATION

Yes, AA

A 5 ft lady casts a shadow that is 22 ft long. Her son is standing next to her and casts a shadow that is 10 ft long. How tall is her son?