COT 1-MMREYES2022-RECORD1.pptx

solving corresponding parts of congruent triangles.

1. Good Morning Class! Hi! I’m Teacher Melissa

2. Hi students! Let’s make Math fun and exciting!

3. TRIANGLES – the strongest shape!

4. SOLVING CORRESPONDING PARTS OF CONGRUENT TRIANGLES MATHEMATICS 8 - QUARTER 3 – WEEK 5 M8GE-IIIf-1 Prepared by: MELISSA M. REYES SST-III/ Math Teacher

5. Objective: Solves corresponding parts of congruent triangles. At the end of the lesson, you are expected to: 1. Identify parts of congruent triangles. 2. Solves corresponding parts of congruent triangles; and 3. Appreciate the application of congruent triangles in real-life situations.

6. Theorem: Corresponding Parts of Congruent Triangles are Congruent (CPCTC) Triangles are congruent if all corresponding sides and angles are congruent. If we prove two triangles are congruent, then we can state that any of their corresponding parts are congruent.

7. EXAMPLE #1 A B C D E F If ΔABC ΔDEF, name the congruent angles and sides. Then draw the triangles, using arcs and slash marks to show the congruent angles and sides.  

8. A B C D E F First, name the three pairs of congruent angles by looking at the order of the vertices in the statement ΔABC ΔDEF  

9. So, A D, B E, and C F.   Since A corresponds to D, and B corresponds to E. AB DE   Since B corresponds to E , and C corresponds to F. BC EF   Since A corresponds to D, and C corresponds to F. AC DF  

10. A B C D E F ΔABC ΔDEF Read as “triangle ABC is congruent to triangle DEF.” Symbol for congruency Δ Symbol for triangle.   The congruent corresponding are marked identically. Can you name the corresponding congruent sides? Corresponding congruent angles? Congruent sides: AB DE, BC EF, AC DF Congruent Angles:   A D, B E, and C F.  

11. EXAMPLE #2 D O G 40° 50° 90° T A C 2x +10° Δ DOG is congruent to Δ CAT. Find the value of x. Since Δ DOG , the corresponding part are congruent wherein O A .  

12. O A   m O m A   50 = 2x + 10 Substitution 50 - 10 = 2x + 10 – 10 Subtract 10 from each side 40 = 2x 40 = 2x 2 = 2 Divide each side by 2 2 0 = x

13. D O G 40° 50° 90° T A C 2x +10° 20 = x 2x +10° Substitute the value of x 2(20) +10° 40 +10° 50° m A = 50°

14. EXAMPLE #3 J F H G 2y – 3 6x + 8 2.5 35° In th e diagram, Δ FHJ Δ HFG . Find the value of x and y.   What part of the triangles are congruent? How do we solve for the value of x and y?

15. So, F H, J G, and H F.   Since F corresponds to H, and H corresponds to F, FH HF   Since H corresponds to F, and J corresponds to G, HJ FG   Since F corresponds to H, and J corresponds to G, FJ HG   a.

16. FJ HG   2y – 3 = 2.5 Substitution 2y -3 + 3 = 2.5 + 3 Add 3 from each side 2y = 5.5 2y = 5.5 2 = 2 Divide each side by 2 y = 2.75 b.

17. J F H G 2y – 3 6x + 8 2.5 35° y = 2.75 FJ = 2y – 3 = 2.5 Substitute the value of y. 2(2.75) – 3 = 2.5 5.5 – 3 = 2.5 2.5 = 2.5 m FJ = 2.5

18. F H   m F m H   6x + 8 = 35 Substitution 6x +8 – 8 = 35 – 8 Subtract 8 from each side 6x = 27 6x = 27 6 = 6 Divide each side by 6 x = 4.5

19. J F H G 2y – 3 6x + 8 2.5 35° x = 4.5 F = 6x + 8 = 35° Substitute the value of x. 6(4.5) + 8 = 35° 27 + 8 = 35° 35° = 35° m F = 35°

20. EXAMPLE #4 J H K G M If K = 68° and J = x + 10, find the exact value of x. K + M+ G = 180° H + J+ G = 180° There fore we can say that K + J+ G = 180° Substitute the value x 68 + x + 10 + x = 180° Combine like terms 68 + 10 + x + x = 180° 78 + 2x = 180° Subtract both sides by 78 to remain 2x only Add like terms 78 – 78 + 2x = 180° - 78 2x = 102 Divide both sides by 2 to remain x only 2 = 2 x = 51

21. If K = 68° and J = x + 10, find the exact value of J and G. To solve for the value of J J = x + 10 J = 51 + 10 J = 61° To solve for the value of G G = x G = 51 K + M+ G = 180° H + J+ G = 180° Therefore: 68 + 61 + 51 = 180° 68 + 61 + 51 = 180°

22. ACTIVITY TIME! Given: Δ BOY Δ GRL; solve for the value of x and y, then find the measure of missing parts of congruent triangles.   O G L R B Y 12 (3y – 6)° 48° 15 2x + 3 93° 11

23. ANSWER! Given: Δ BOY Δ GRL; solve for the value of x and y, then find the measure of missing parts of congruent triangles.   O G L R B Y 12 (3y – 6)° 48° 15 2x + 3 93° 11

24. Corresponding sides Corresponding angles BO = GR Answer: BY = GL O Y = RL B = G Y = L O = R BO = GR For: 2x + 3 = 11 2x + 3 – 3 = 11- 3 2x = 8 2 = 2 x = 4 For: BY = GL BY = 12 O Y = RL 15 = RL For: B = G 93 = 3y – 6 93 + 6 = 3y – 6 + 6 99 = 3y 3 = 3 33 = y BO = 2x +3 BO = 2 (4) + 3 BO = 8 + 3 BO = 11 G = 3y – 6 G = 3 (33) – 6 G = 99 – 6 G = 93 For: Y = L O = R O = 48° L = 39 °

25. Theorem: Corresponding Parts of Congruent Triangles are Congruent (CPCTC) Triangles are congruent if all corresponding sides and angles are congruent. If we prove two triangles are congruent, then we can state that any of their corresponding parts are congruent. Remember!

26. Individual Activity Given: Δ DEF Δ XYZ; solve for the measure of missing parts of congruent triangles.   73° 23 cm E F D 25 cm 47° Y X Z 22 cm

27. That ends our Lesson for today! Study our next Lesson: Proving two triangles are congruent. Good day Everyone!