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Getting Started… 9.5 Congruence

2 ft. 2 ft. 1 ft. 2 ft. 4 ft. 1 ft. 1 ft. 1 ft. 2 ft. 1 ft. 3 ft. Getting Started… 9.5 Congruence. Find the area of the blue region. Assume all angles are right angles. 1 ft. 31 square ft. Congruence Lesson 9.5. D. I. H. E. J. P. C. A. K. B.

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Getting Started… 9.5 Congruence

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  1. 2 ft. 2 ft. 1 ft. 2 ft. 4 ft. 1 ft. 1 ft. 1 ft. 2 ft. 1 ft. 3 ft. Getting Started…9.5 Congruence Find the area of the blue region. Assume all angles are right angles. 1 ft. 31 square ft

  2. Congruence Lesson 9.5

  3. D I H E J P C A K B Naming & Comparing Polygons • List vertices in order, either clockwise or counterclockwise. • When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction. • By doing this you can identify corresponding parts. DCBAE D corresponds to I AE corresponds to PH IJKPH

  4. 10 D E C A B • How many ways can you name pentagon DCBAE? Do it. Pick a vertex and go clockwise Pick a vertex and go counterclockwise DEABC CDEAB BCDEA ABCDE EABCD DCBAE CBAED BAEDC AEDCB EDCBA

  5. Polygon Congruence • If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent.

  6. A B E F D H C G CONGRUENCE STATEMENT ~ ABCD = EFGH Congruence Statements • These polygons are congruent. • Remember, if they are congruent, they are EXACTLY the same. • That means that all of the corresponding angles are congruent and all of the corresponding sides are congruent.

  7. X ~ YM = < XML = <MLX = XY = ML ~ < XMY ~ <MYX ~ L XL Y M

  8. Congruent Angles • Definition: they have the same degree measure. • Symbols: angle A congruent angle B if and only if m a and m b • Picture: 30° • B 30° A

  9. The first relationship we are going to talk about 1 3 4 2 Vertical Angles Definition: Two angles are vertical angles if their sides form two pairs of opposite rays Vertical angles are always congruent. Angles 1 and 2 are vertical angles Angles 3 and 4 are also vertical angles

  10. What is the measure of the angle? 5y – 50 4y – 10 5y – 50 = 4y – 10 y = 40 Plug y back into our angle equations and we get

  11. Find the value of x in each figure • 1. 2. • 3. 4. 130° 5x° 25° x° 125 ° x° 40° (x – 10)°

  12. Identify each pair of angles as adjacent, vertical, complementary, and/or supplementary. Example 1: 3 2 4 1 ADJACENT 5

  13. Identify each pair of angles as adjacent, vertical, complementary, and/or supplementary. Example 2: 3 2 4 1 VERTICAL 5

  14. Identify each pair of angles as adjacent, vertical, complementary, and/or supplementary. Example 3: 3 2 4 1 ADJACENT, COMPLEMENTARY 5

  15. Identify each pair of angles as adjacent, vertical, complementary, and/or supplementary. Example 4: 3 2 4 ADJACENT, SUPPLEMENTARY 1 5

  16. Find x, y, and z. Example 5: x = 129, y = 51, z = 129

  17. L T P A O Find x. X = 8

  18. L T P A O Find Since we have already found the value of x, all we need to do now is to plug it in for LAT. 155

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