Warm-Up

For use after Lesson 4.7 & 4.8

1. Find m 3.

18°ANSWER

2. How do you know that a and b are parallel?

Both are perpendicular to c.

ANSWER

Daily Homework Quiz

1. The vertices GHI and RST are G(–2, 5), H(2, 5),

I(–2, 2), R(–9, 8), S(–5, 8), and T(–9, 5). Is GHI RST? Explain.

Yes. GH = RS = 4, HI = ST = 5, and IG = TR = 3. By the SSS post ., it follows that GHI RST.

ANSWER

Is ABC XYZ? Explain.2.

Yes. By the seg. Add. Post., AC XZ. Also , AB XY and BC YZ. So ABC XYZ by the SSS post.

ΔQRS Δ__________

Q

R S T

U

10 10

Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

1. ABE, CBD

ANSWER SAS Post.

Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

2. FGH, HJK

ANSWER HL Thm.

State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate.

3. ST YZ, RS XY

ANSWER S Y.

EXAMPLE 1 Use the SAS Congruence Postulate

Write a proof.

GIVEN

PROVE

STATEMENTS REASONS

BC DA, BC AD

ABC CDA

1. Given1. BC DAS

Given2. 2. BC AD

3. BCA DAC 3. Alternate Interior Angles Theorem

A

4. 4. AC CA Reflexive Property of Congruence

S

ABC CDA 5. SAS

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem

Write a proof.

SOLUTION

Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram.

GIVEN WY XZ, WZ ZY, XY ZY

PROVE WYZ XZY

STATEMENTS REASONS

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem

1. WY XZ 1. Given

4. 4. Definition of a right triangle

WYZ and XZY are right triangles.

L ZY YZ5. 5. Reflexive Property of Congruence

6. WYZ XZY 6. HL Congruence Theorem

3. 3. Definition of linesZ and Y are right angles

2. 2. WZ ZY, XY ZY Given

EXAMPLE 1 Identify congruent triangles

Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem.

a.

EXAMPLE 1 Identify congruent triangles

b. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent.

c. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate.