Geometry Chapter 4 Review

Classification of Triangles

Angles Sides

Geometry Chapter 4 Review

Classify triangles by angles:

1. The measure of two angles are 35 and 55.

Geometry Chapter 4 Review

Classify triangles by angles:

1. The measure of two angles are 35 and 55.

2. The measures of two angles are 70 and 50.

Geometry Chapter 4 Review

Classify triangles by angles:

1. The measure of two angles are 35 and 55.

2. The measures of two angles are 70 and 50.

3. The measure of one acute angle of a right triangle is 3/2 the measure of the other acute angle.

Find the measure of each acute angle.

Geometry Chapter 4 Review

Classify triangles by angles:

1. The measure of two angles are 35 and 55.

2. The measures of two angles are 70 and 50.

3. The measure of one acute angle of a right triangle is 3/2 the measure of the other acute angle.

Find the measure of each acute angle.

4. ABC is isosceles with: AC = AB, AC = 4x - 2 AB = 2x + 6, BC = 3x - 1Find BC.

Geometry Chapter 4 Review

Prove the 180 Theorem

Geometry Chapter 4 Review

THIRD ANGLE Theorem –

If TWO Angles of one Triangle are CONGRUENT to

TWO Angles of a second triangle,

then the THIRD angles of the triangles

ARE CONTRUENT.

Geometry Chapter 4 Review

EXTERIOR ANGLE Theorem –

The measure of an EXTERIOR Angle of a Triangle

is EQUAL to

the SUM of the Measures of the TWO REMOTE Interior Angles.

Geometry Chapter 4 Review

Using the figure at the right, answer the following : If m 4 is 140, then m 2 = _______ 

AB

C

DE

12 3 4

Geometry Chapter 4 Review

Using the figure at the right, answer the following : If m C = 72, then the m 1 = ________

AB

C

DE

12 3 4

Geometry Chapter 4 Review

Using the figure at the right, answer the following : If m 2 = 34, then m 4 = __________

AB

C

DE

12 3 4

Geometry Chapter 4 Review

Definition: COROLLARY

A statement that can be easily proved using a theoremis called a COLOLLARY.

1. The ACUTE ANGLES of a right triangle are COMPLEMENTARY.

2. There can be at most one right or obtuse angle in a triangle.

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

A B

C

D E

F

The way you NAME the Triangle establishes theCORRESPONDENCE:

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

SO, if ABC FGH:

Congruent Angles Congruent Sides

Be sure to WRITE the LETTERS of VERTICESin the CORRECT ORDER when you write a Statement.

Geometry Chapter 4 ReviewY T

P

H

G L

Given:

Y LP HT G

Are these Triangles CONGRUENT?

To Prove Triangles are CONGRUENT:

• Prove CORRESPONDING Sides and CORRESPONDING Angles are CONGRUENT

• Prove COORESPONDING SIDES are CONGRUENT (SSS)

• Prove Two CORRESPONDING Angles and the INCLUDED SIDE are CONGRUENT (ASA)

• Prove Two CORRESPONDING Sides and the INCLUDED ANGLE are CONGRUENT (SAS)

• Prove Two CORRESPONDING Angles and a NONIncluded Side are CONGRUENT (AAS)

Geometry Chapter 4 Review

Given:

Are these Triangles CONGRUENT?

YT LGPT HG

T G

Y T

P

H

G L

Geometry Chapter 4 Review

Given:

Are these Triangles CONGRUENT?

P HPT HG

T G

Y T

P

H

G L

Geometry Chapter 4 Review

Given:

Y LT G

m P = 3x - 40m H x 20

m PFind:

Y T

P

H

G L

Geometry Chapter 4 Review

Given: RST XYZ

ST = 2x + 13YZ = 4x + 5TR = 3x - 1

Find ZX:

Geometry Chapter 4 Review

P

M T

Q

Given:

PQ bisects MPTPQ bisects MQT

Prove:

PMQ PTQ

Triangle MNO is both equilateral and equiangular.Triangle PQR has 3 congruent sides, m P = 60and m Q = 60.

Is Triangle MNO PQR?

Geometry Ch 4 Review CPCTC THEOREM

RECALL:

2 triangles are CONGRUENT, IF:

Their CORRESPONDING Sides are Congruent

AND

Their CORRESPONDING Angles are Congruent.

Geometry Ch 4 Review CPCTC THEOREM

THEREFORE, it follows:

IF --

two triangles can be proved Congruent,

THEN --

Any pair of Corresponding sides or pair ofCorresponding Angles are Congruent.

Geometry Ch 4 Review CPCTC THEOREM

This is abbreviated:

Corresponding Parts of Congruent Triangles

are Congruent.

C P C T C

Geometry Chapter 4 Review

T

K

Y

UG

H

Given:

TU GYKY ||HUKT TGHG TG

Prove: K H

Geometry Ch 4 Review Example of CPCTC

P

S

Q

R

Given: PS PQSR QR

Prove: SPR QPR

Geometry Ch 4 Review

Geometry Ch 4 ReviewAnother Example of Using CPCTC

1 3

5 6

4 2

B F C

E

Given: EF bisects BECBE CE

Prove: 1 2

Geometry Ch 4 Review Yet ANOTHER Example

A

D

B

E

C

Given: AB BCAD BEAD ||BE

Prove: BD || CE

Geometry Ch 4 Review FINAL CPCTC Example

A B

E

C D

Given: AB|| CDAB CD

Prove: E is midpoint of AD

Geometry Ch 4 Review

Geometry Ch 4 Review

Geometry Ch 4 Review

Geometry Ch 4 Review

TP

R

W

Q

MS

Prove: PWQ MRQ

Geometry Ch 4 Review