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Warm Up. 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 B Review. Congruent Triangles. Congruent triangles have 3 congruent sides and 3 congruent angles.

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Warm Up

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Warm Up

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


Complete each congruence statement.

B

If ABC  DEF,

then BC  ___

A

C

D

F

E


Fill in the blanks

If CAT  DOG,

then AC  ___


Fill in the blanks

BCA   ____

____   GFE


There are 5 ways to prove triangles congruent.


We Use

  • 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)


There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg

HL


SSS

SAS

ASA

AAS

HL

NO BAD WORDS

The ONLY Ways To Prove Triangles Are Congruent


2 markings you can add if they aren’t marked already


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


Which shapes are similar and how do you know?

1.

3.

2.


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


Remember-Congruent

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


Are these Triangles similar? If so, name the postulate.

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?


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