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**5-6 Congruence Warm Up Problem of the Day Lesson Presentation**

Pre-Algebra

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**5-6 Congruence Warm Up Find the measure of the indicated angle.**

Pre-Algebra 5-6 Congruence Warm Up Find the measure of the indicated angle. 1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75° 55° 2. the third angle of a right triangle with an angle of 60° 30° 3. the supplement of a 35° angle 145°

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Problem of the Day The measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle? mABC = 38°; m CBD = 52°

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**Learn to use properties of congruent figures to solve problems.**

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Vocabulary correspondence

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**A correspondence is a way of matching up two sets of objects.**

If two polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices in the second polygon are written in order of correspondence with the first polygon.

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**Additional Example 1A: Writing Congruent Statements**

Write a congruence statement for the pair of polygons. The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence. Q, so A corresponds to Q. R, so B corresponds to R. P, so C corresponds to P. The congruence statement is triangle triangle QRP.

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**Additional Example 1B: Writing Congruent Statements**

Write a congruence statement for the pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. M, so D corresponds to M. N, so E corresponds to N. O, so F corresponds to O. P, so G corresponds to P. Q, so H corresponds to Q. The congruence statement is pentagon pentagon MNOPQ.

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**Write a congruence statement for the pair of polygons.**

Try This: Example 1A Write a congruence statement for the pair of polygons. The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence. A B | 60° 60° || |||| 120° 120° D ||| C S, so A corresponds to S. Q R ||| 120° 120° T, so B corresponds to T. || |||| Q, so C corresponds to Q. 60° 60° | R, so D corresponds to R. T S The congruence statement is trapezoid trapezoid STQR.

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**Write a congruence statement for the pair of polygons.**

Try This: Example 1B Write a congruence statement for the pair of polygons. The vertices in the first pentagon are written in order around the pentagon starting at any vertex. 110° A B M, so A corresponds to M. 110° N, so B corresponds to N. F 140° 140° C 110° O, so C corresponds to O. 110° E D P, so D corresponds to P. N 110° O Q, so E corresponds to Q. M 110° 140° L, so F corresponds to L. 140° 110° P L The congruence statement is hexagon hexagon MNOPQL. 110° Q

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**Additional Example 2A: Using Congruence Relationships to Find Unknown Values**

In the figure, quadrilateral quadrilateral JKLM. A. Find a. a + 8 = 24 KL a = 16 –8 –8 Subtract 8 from both sides.

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**Additional Example 2B: Using Congruence Relationships to Find Unknown Values**

In the figure, quadrilateral quadrilateral JKLM. B. Find b. 6b = 30 YX 6b = 30 Divide both sides by 6. b = 5

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**Additional Example 2C: Using Congruence Relationships to Find Unknown Values**

In the figure, quadrilateral quadrilateral JKLM. C. Find c. 5c = 85 V 5c = 85 Divide both sides by 5. c = 17

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Try This: Example 2A In the figure, quadrilateral quadrilateral QRST. A. Find a. 3a = 6 RS 3a = 6 Divide both sides by 3. 3a I H a = 2 6 4b° R S 120° J 30° Q K c + 10° T

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Try This: Example 2B In the figure, quadrilateral quadrilateral QRST. B. Find b. 4b = 120 S 4b = 120 Divide both sides by 4. 3a I H b = 30° 6 4b° R S 120° J 30° Q K c + 10° T

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Try This: Example 2C In the figure, quadrilateral quadrilateral QRST. C. Find c. c + 10 = 30 T –10 –10 c + 10 = 30 Subtract 10 from both sides. 3a I H c = 20° 90° 6 4b° R S 90° 120° J 30° Q c + 10° K T

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**Explain what it means for two polygons to be congruent.**

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What’s the Error? Explain the error in the congruence statement and write a correct congruence statement. B E 60˚ 60˚ 30˚ 30˚ A F C D Triangle ABC triangle DEF

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Lesson Quiz In the figure, ABCD 1. Find XY. 10 2. Find mB. 80° 3. Find CD. 8 4. Find mZ. 90°

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Congruent Polygons 4.1.

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