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EXAMPLE 3 PowerPoint PPT Presentation


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WYZ 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.

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EXAMPLE 3

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Example 3

WYZXZY

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


Example 3

STATEMENTS

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


Example 3

EXAMPLE 4

Choose a postulate or theorem

Sign Making

You are making a canvas sign to hang on the triangular wall over the door to the barn shown in the picture. You think you can use two identical triangular sheets of canvas. You knowthatRP QS and PQ PS. What postulate or theorem can you use to conclude that

PQRPSR?


Example 3

You are given that PQ PS. By the Reflexive Property, RP RP. By the definition of perpendicular lines, both

RPQ and RPSare right angles, so they are congruent. So, two sides and their included angle are congruent.

ANSWER

You can use the SAS Congruence Postulate to conclude that .

PQRPSR

EXAMPLE 4

Choose a postulate or theorem

SOLUTION


Example 3

Redraw ACBand DBCside by side with corresponding parts in the same position.

for Examples 3 and 4

GUIDED PRACTICE

Use the diagram at the right.


Example 3

BC CB

L

Reflexive Property of Congruence

ACBDBC

HL Congruence Theorem

for Examples 3 and 4

GUIDED PRACTICE

STATEMENTS

REASONS


Example 3

STATEMENTS

REASONS

AC DB

Given

AB BC, CD BC

Given

Definition of lines

C B

Definition of a right triangle

ACBand DBC are right triangles.

for Examples 3 and 4

GUIDED PRACTICE

Use the diagram at the right.

Use the information in the diagram to prove that

ACBDBC


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