Mathematics 8 Quarter-3-Module-5 MELCS based

Math 8

1. Mathematics 8 Quarter 3 – Module 5 March 15, 2022 Solving Corresponding Parts of Congruent Triangles

2. Prayer

3. Which pair of triangles are congruent? 1 7 2 4 6 5 8 3

4. Which pair of triangles are congruent? 1 7 2 3 4 6 5 8

5. Solving Corresponding Parts of Congruent Triangles

6. B R I D G E

7. Solving Congruent Parts of a Triangles Triangles are widely used in our structures. Bridge is one of them. Triangles make the structure sturdy (strongly and solidly built). San Juanico Bridge is one of them. San Juanico Bridge, known as the longest bridge in the Philippines, begun its construction in 1969 and finished in 1973. It costs some $22M (Php 154 M in the 70’s). This bridge ranges 2.2 kilometers and connects the twin island of Leyte and Samar. It even withstood the power of typhoon Yolanda in 2013 and very evident that it contributes to the economic growth and love of the two islands.

8. Solving Congruent Parts of a Triangles Triangles are widely used in our structures. Bridge is one of them. Triangles make the structure sturdy (strongly and solidly built). San Juanico Bridge is one of them. San Juanico Bridge, known as the longest bridge in the Philippines, begun its construction in 1969 and finished in 1973. It costs some $22M (Php 154 M in the 70’s). This bridge ranges 2.2 kilometers and connects the twin island of Leyte and Samar. It even withstood the power of typhoon Yolanda in 2013 and very evident that it contributes to the economic growth and love of the two islands.

9. Illustrative Examples: A. The triangles shown below are congruent. 1. Find   2. Find   3. Find   1. Find     By the definition of congruent segments, the measurements of the sides are equal.  

10. Illustrative Examples: A. The triangles shown below are congruent. 1. Find   2. Find   3. Find   2. Find     By the definition of congruent segments, the measurements of the sides are equal.  

11. Illustrative Examples: A. The triangles shown below are congruent. 1. Find   2. Find   3. Find   3. Find     By the definition of congruent segments, the measurements of the sides are equal.   Congruent segments have equal measurements.

12. Illustrative Examples: B. In the figure,   1. Find   2. Find   3. Find     By the definition of congruent angles, the measurements of the angles are equal. ∠𝑇𝐴𝐻 =   1. Find  

13. Illustrative Examples: B. In the figure,   1. Find   2. Find   3. Find     By the definition of congruent angles, the measurements of the angles are equal. ∠M   2. Find  

14. Illustrative Examples: B. In the figure,   1. Find   2. Find   3. Find     ∠M𝐻 A   3. Find   The total measurement of the interior angles of a triangle is 180°.

15. Illustrative Examples: C. Without an illustration, suppose The perimeter of is 81mm, = 15mm, = 37mm, m C = 37 and m = 56 Find the following:   1.   Perimeter of a Triangle = + +   81= + +   81= +   = 29mm  

16. Illustrative Examples: C. Without an illustration, suppose The perimeter of is 81mm, = 15mm, = 37mm, m C = 37 and m = 56 Find the following:   2.     = 29mm   3.     = 15mm  

17. Illustrative Examples: C. Without an illustration, suppose The perimeter of is 81mm, = 15mm, = 37mm, m C = 37 and m = 56 Find the following:   4.     = 37mm   5.m   B C   B = 37  

18. Illustrative Examples: C. Without an illustration, suppose The perimeter of is 81mm, = 15mm, = 37mm, m C = 37 and m = 56 Find the following:   6. m   m B + m G + M = 180   37 + m G+ 56 = 180   93 + m G = 180   m G = 87   7.m   G H   H = 87  

19. D. Given: ∆RPA ≅ ∆NUJ, RP = 2x + 5 and NU = 13. Find the value of x.   2x + 5 = 13 2x = 13 -5 2x = 8 2 2 x = 4 Illustrative Examples:

20. Illustrative Examples: E. Given: ∆ACN ≅ ∆GMP, m A = (3x – 10) ° and m G = 32°. Find the value of x.   A G   3x - 10 ° = 32 ° 3x =42 3 3 x = 14 3x = 32+10

21. Illustrative Examples: F. Given: ∆HPE ≅ ∆HPO, EH = (4x + 5) mm and OH = (3x + 12) mm.   4X + 5 = 3X + 12 x = 7 4X – 3X = 12 - 5 Find the value of x. What is EH and OH? EH = 4x + 5 EH = 4(7) + 5 EH = 33 OH = 3x + 12 OH = 3(7) + 12 OH = 33

22. Illustrative Examples: G. Given: ∆GKN ≅ ∆PNK, m G = (5x – 16) ° and m P=2X+32°.Find the value of x.Find m G and m P   G P   5x - 16 ° = 2X + 32 ° 3x =48 3 3 x = 16 5x - 2X = 32 + 16

23. Illustrative Examples: G. Given: ∆GKN ≅ ∆PNK, m G = (5x – 16) ° and m P=2X+32°.Find the value of x.Find m G and m P   m G = (5x – 16) °   m G = [5(16) – 16] °   m G = 80 – 16   m G = 64 °  

24. Illustrative Examples: G. Given: ∆GKN ≅ ∆PNK, m G = (5x – 16) ° and m P=2X+32°.Find the value of x.Find m G and m P   m P = (2x + 32) °   m P = [2(16) + 32]°   m G = 32+32   m G = 64 °  

25. = ____ = ____ = ____ = ____ = ____ m = ____ a = ____ m = ____ m = ____ The perimeter of ∆DOG is 82cm, find .   1. ∆CAT ≅ ∆DOG, find the following measurement 7y 3 y + 20 5a 2a + 3 3 18 5 35 35 9   1 5   85   29cm

26. = ____ = ____ = ____ = ____ = ____ m = ____ a = ____ m = ____ m = ____ The perimeter of ∆DOG is 82cm, find .   1. ∆CAT ≅ ∆DOG, find the following measurement 7y 3 y + 20 5a 2a + 3 3 18 5 35 35 9   1 5   85   29cm

27. 2. ∆WXV ≅ ∆ZYV, find the following measurement b c d e

28. 2. ∆WXV ≅ ∆ZYV, find the following measurement 84   5   4   4   4   4   5