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4.9 (M1) Prove Triangles Congruent by SAS & HLPowerPoint Presentation

4.9 (M1) Prove Triangles Congruent by SAS & HL

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Presentation Transcript

Vocabulary

- In a right triangle, the sides adjacent to the right angle are the legs.
- The side opposite the right angle is the hypotenuse.
- Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.

- Hypotenuse-Leg (HL) Congruence Theorem – If the hypotenuse and one leg of a right triangle are congruent to they hypotenuse and leg of another right triangle, the triangles are congruent.

1. why.

ABE,CBD

ANSWER

SAS Post.

Daily Homework Quiz

For use after Lesson 4.4

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

2. why.

FGH,HJK

ANSWER

HL Thm.

Daily Homework Quiz

For use after Lesson 4.4

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

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

3.

ST YZ, RS XY

ANSWER

SY.

Daily Homework Quiz

For use after Lesson 4.4

BC DA why.,BC AD

ABCCDA

ABCCDA

STATEMENTS

REASONS

S

BC DA

Given

Given

BC AD

BCADAC

A

Alternate Interior Angles Theorem

S

ACCA

Reflexive Property of Congruence

EXAMPLE 1

Use the SAS Congruence Postulate

Write a proof.

GIVEN

PROVE

5.

5. SAS Congruence Post.

WYZ why.XZY

PROVE

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

EXAMPLE 3

Use the Hypotenuse-Leg Congruence Theorem

Write a proof.

GIVEN

WY XZ,WZ ZY, XY ZY

SOLUTION

STATEMENTS why.

REASONS

WY XZ

Given

WZ ZY, XY ZY

Given

Definition of lines

Z andY are right angles

Definition of a right triangle

WYZand XZY are right triangles.

ZY YZ

L

Reflexive Property of Congruence

WYZXZY

HL Congruence Theorem

EXAMPLE 3

Use the Hypotenuse-Leg Congruence Theorem

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