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Understanding Congruence and Angle Measures in Geometry

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liko
17 diapositives · 333 Views · Aug 04, 2014

This lesson focuses on congruence in geometric figures and angle measures. Students will learn how to find angles in different scenarios, including quadrilaterals and triangles, and how to write congruence statements for pairs of polygons. Examples cover calculating the unknown angle measurements based on given values and understanding the properties of congruent shapes. Engage in practical exercises to reinforce learning, applying knowledge of correspondence between angles and sides in congruent figures. Perfect for reinforcing geometry skills in Grades 5-6.

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Understanding Congruence and Angle Measures in Geometry
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  1. 5-6 Congruence Warm Up Problem of the Day Lesson Presentation Course 3

  2. 5-6 Congruence Course 3 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°

  3. 5-6 Congruence Course 3 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? mABC = 38°; mCBD = 52°

  4. 5-6 Congruence Course 3 Learn to use properties of congruent figures to solve problems.

  5. 5-6 Congruence Course 3 Vocabulary correspondence

  6. 5-6 Congruence Course 3 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.

  7. 5-6 Congruence 55 55 Course 3 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. A@Q, so A corresponds to Q. B@R, so B corresponds to R. C@P, so C corresponds to P. The congruence statement is triangle ABC@ triangle QRP.

  8. 5-6 Congruence Course 3 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. D@M, so D corresponds to M. E@N, so E corresponds to N. F@O, so F corresponds to O. G@P, so G corresponds to P. H@Q, so H corresponds to Q. The congruence statement is pentagon DEFGH@ pentagon MNOPQ.

  9. 5-6 Congruence Course 3 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 A@S, so A corresponds to S. Q R ||| 120° 120° B@T, so B corresponds to T. || |||| C@Q, so C corresponds to Q. 60° 60° | D@R, so D corresponds to R. T S The congruence statement is trapezoid ABCD@ trapezoid STQR.

  10. 5-6 Congruence Course 3 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 A@M, so A corresponds to M. 110° 140° 140° F B@N, so B corresponds to N. C 110° C@O, so C corresponds to O. E 110° D N D@P, so D corresponds to P. 110° O M E@Q, so E corresponds to Q. 140° 110° 110° F@L, so F corresponds to L. P 140° L The congruence statement is hexagon ABCDEF@ hexagon MNOPQL. 110° Q

  11. 5-6 Congruence WX @ KL a + 8 = 24 –8 –8 a = 16 Course 3 Additional Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. A. Find a. Subtract 8 from both sides.

  12. 5-6 Congruence ML @ YX 6b = 30 6b = 30 6 6 Course 3 Additional Example 2B: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. B. Find b. Divide both sides by 6. b = 5

  13. 5-6 Congruence J @V 5c = 85 5c = 85 5 5 Course 3 Additional Example 2C: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY@ quadrilateral JKLM. C. Find c. Divide both sides by 5. c = 17

  14. 5-6 Congruence IH @ RS 3a = 6 3a = 6 3 3 Course 3 Try This: Example 2A In the figure, quadrilateral JIHK@ quadrilateral QRST. A. Find a. Divide both sides by 3. 3a I H a = 2 6 4b° S R 120° J 30° Q K c + 10° T

  15. 5-6 Congruence H @S 4b = 120 4b = 120 4 4 Course 3 Try This: Example 2B In the figure, quadrilateral JIHK@ quadrilateral QRST. B. Find b. Divide both sides by 4. 3a I H b = 30° 6 4b° S R 120° J 30° Q K c + 10° T

  16. 5-6 Congruence K @T c + 10 = 30 c + 10 = 30 –10 –10 Course 3 Try This: Example 2C In the figure, quadrilateral JIHK@ quadrilateral QRST. C. Find c. Subtract 10 from both sides. 3a I H c = 20° 6 90° 4b° S R 120° 90° J 30° c + 10° Q K T

  17. 5-6 Congruence 1. Find XY. 3. Find CD. Course 3 Lesson Quiz In the figure, WXYZ@ABCD 10 80° 2. Find mB. 8 90° 4. Find mZ.