4.4 - Prove Triangles Congruent by SAS and HL

Included Angle:Angle in-between two congruent sides

1. Use the diagram to name the included angle between the given pair of sides.

and GH HI

H

1. Use the diagram to name the included angle between the given pair of sides.

HIG

and HI IG

1. Use the diagram to name the included angle between the given pair of sides.

JGI

and JG IG

Side-Angle-Side (SAS) Congruence Postulate

A B C D4cm 4cm

E F

CDAB

CFAE

CA

If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________

included

congruent

congruent

Right Triangles:

leg

leghypotenuse

Hypotenuse-Leg (HL) Congruence Theorem:

If the _______________ and a ________ of a ___________ triangle are ____________ to the _____________ and ________ of a second _________ triangle, then the twotriangles are _________________.

hypotenuse legright congruent

hypotenuse legright

congruent

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SSS

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SSS

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SAS

2. Decide whether the triangles are congruent. Explain your reasoning.

No, AD ≠ CD

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SAS

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, HL

2. Decide whether the triangles are congruent. Explain your reasoning.

No, Not a right triangle

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SSS

2. Decide whether the triangles are congruent. Explain your reasoning.

Yes, SAS

3. State the third congruence that must be given to prove ABC DEF.

GIVEN: B E, , ______ ______. Use the SAS Congruence Postulate.

EFBC BA ED

3. State the third congruence that must be given to prove ABC DEF.

GIVEN: , ______ ______. Use the SSS Congruence Postulate.

EFBCDEAB , AC DF

3. State the third congruence that must be given to prove ABC DEF.

GIVEN: A is a right angle and A D. Use the HL Congruence Theorem.

,DFAC

EFBC

4. Given: Prove: ∆RGI ∆TGH

1. 1. given

2. 2. Def. of midpt

3. 3. Def. of midpt

4. 4.

5. 5.

Vertical angles

GIHG

RGI TGH

∆RGI ∆TGH

is the midpoint of and G RT HI

is the midpoint of and G RT HI

RG GT

SAS

5. Given:

Prove: ∆ABD ∆CDB

CDAB

CDAB

Statements Reasons

CDAB Given

D

A

B

C

1. 1.

D

A

B

C

CDAB

CDAB

CDAB Given

CDAB

CDB ABD Alternate Interior Angles

Given

∆ABD ∆CDB SAS

DBDB Reflexive

D

A

B

C

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Statements Reasons

5. Given:

Prove: ∆ABD ∆CDB

6. Given:

Prove: ∆ACD ∆ACB

A

BCD

bisects AC DAB

DA BA

Given

Def. of Angle Bisector

Given

∆ACD ∆ACB SAS

AC AC Reflexive

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Statements Reasons bisects AC DAB

DA BA

DAC BAC

7. Given:

Prove: ∆ACD ∆ACB

AD ABAC BD

A

BCD

GivenGiven

Def. of perp. lines

Reflexive

ACD ACB All right angles are

1. 1.2. 2.

3. 3.

4. 4.

5. 5.

Statements ReasonsAD ABAC BD

∆ACD ∆ACB HL6. 6.

ACD and ACB are right angles

AC AC

Ans: BC EF

HW ProblemSectio

nPage # Assignment Spiral ?

s

4.4 243 3-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all)

9-11

# 27

HW ProblemSectio

nPage # Assignment Spiral ?

s

4.4 243 3-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all)

9-11

# 26