POSTULATES ON TRIANGLE CONGRUENCE.pptx

Side-Angle-Side Triangle Postulate
Angle-Side-Angle Triangle Postulate
Angle-Side-Angle Triangle Postulate
Corresponding Parts of Congruent Triangles are Congruent CPCTC
Two triangles are congruent if and only if their corresponding parts are congruent to each other.
Grade 8 Mathematics Third Quarter

1. POSTULATES ON TRIANGLE CONGRUENCE Presenter Name

2. SAS Congruence Postulate (Side-Angle-Side) If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. 9/3/20XX Presentation Title 2

3. Consider below   9/3/20XX Presentation Title 3 Included angle is the angle between two sides of a triangle. is the included angle between and . is the included angle between and is the included angle between a nd .    

4. In and , we can pair the corresponding two sides and the included angle to illustrate that the two triangles are congruent by SAS Congruence Postulate using an if-then statement.   9/3/20XX Presentation Title 4 If (side) (included angle) (side) Then by SAS Congruence Postulate    

5. S imilarly, we can give the names of the two congruent triangles using SAS Congruence Postulate when it was marked with corresponding congruent parts. 9/3/20XX Presentation Title 5 Congruent Parts: Then        

6. S imilarly, we can give the names of the two congruent triangles using SAS Congruence Postulate when it was marked with corresponding congruent parts. 9/3/20XX Presentation Title 6 Congruent Parts: Then      

7. Given: ∠F ≌ ∠R , bisects Prove: △ FAI ≌ △ RAI   9/3/20XX Presentation Title 7 STATEMENTS REASONS 1. 1. Given 2. ∠F ≌ ∠R 2. Given 3. bisects 3. Given 4. 4. Definition of bisector 5. △ FAI ≌ △ RAI 5. SAS Congruence Postulate STATEMENTS REASONS 1. Given 2. ∠F ≌ ∠R 2. Given 3. Given 4. Definition of bisector 5. △ FAI ≌ △ RAI 5. SAS Congruence Postulate I A F R

8. Given: ⟘ ⟘ E is the midpoint of Prove: △ ABE ≌ △ CDE   9/3/20XX Presentation Title 8 A B E C D STATEMENTS REASONS 1. ⟘ 1. Given 2. ∠B is a right angle 2. Definition of perpendicular lines 3. ⟘ 3. Given 4. ∠D is a right angle 4. Definition of perpendicular lines 5. ∠B ∠D 5. Any two right angles are congruent 6. E is the midpoint of 6. Given 7. 7. Definition of midpoint 8. △ ABE ≌ △ CDE 8. SAS Congruence Postulate STATEMENTS REASONS 1. Given 2. ∠B is a right angle 2. Definition of perpendicular lines 3. Given 4. ∠D is a right angle 4. Definition of perpendicular lines 5. Any two right angles are congruent 6. Given 7. Definition of midpoint 8. △ ABE ≌ △ CDE 8. SAS Congruence Postulate

9. ASA Congruence Postulate (Angle-Side-Angle) If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent. 9/3/20XX Presentation Title 9

10. Refer to ∆JOY again. 9/3/20XX Presentation Title 10 Included side is the common side to two angles of a triangle. is the included side between and is the included side between and . is the included side between and .    

11. Using and , we can illustrate that these two triangles are congruent by ASA Congruence Postulate.   9/3/20XX Presentation Title 11 If (angle) (included side) (angle) Then by ASA Congruence Postulate    

12. Take note that we can also determine the two congruent triangles using ASA Congruence Postulate by just looking at the corresponding congruent parts even without an illustrated figure with markings. 9/3/20XX Presentation Title 12 Consider the following given: Therefore, we can say that by ASA Congruence Postulate. We can draw the two congruent triangles by ASA Congruence Postulate as shown with markings.  

13. Given: Right triangles ABC and PQR with and ∠ A ≌ ∠ P Prove: △ ABC ≌ △ PQR   9/3/20XX Presentation Title 13 STATEMENTS REASONS 1. △ ABC and △ PQR are right triangles 1. Given 2. ∠B ≌ ∠Q 2. All right triangles are congruent 3. 3. Given 4. ∠A ≌ ∠P 4. Given 5. △ ABC ≌ △ PQR 5. ASA Congruence Postulate STATEMENTS REASONS 1. △ ABC and △ PQR are right triangles 1. Given 2. ∠B ≌ ∠Q 2. All right triangles are congruent 3. Given 4. ∠A ≌ ∠P 4. Given 5. △ ABC ≌ △ PQR 5. ASA Congruence Postulate A B C P Q R

14. Given: ∠ 1 ≌ ∠ 2 D is the midpoint of ∠ ADB is a right angle Prove: △ ADB ≌ △ ADC   9/3/20XX Presentation Title 14 STATEMENTS REASONS 1. ∠1 ≌ ∠2 1. Given 2. ∠ABD and ∠1 form a linear pair ∠ACD and ∠2 form a linear pair 2. Definition of linear pair 3. ∠ABD is supplementary to ∠1 ∠ACD is supplementary to ∠2 3. Linear Pair Postulate 4. ∠ABD ≌ ∠ACD 4. Supplements to congruent angles are congruent 5. D is the midpoint of 5. Given 6. 6. Definition of midpoint 7. ∠ADB is a right angle ∠ADC is a right angle 7. Given 8. ∠ADB ≌ ∠ADC 8. Any two right angles are congruent 9. △ ADB ≌ △ ADC 9. ASA Congruence Postulate STATEMENTS REASONS 1. ∠1 ≌ ∠2 1. Given 2. ∠ABD and ∠1 form a linear pair ∠ACD and ∠2 form a linear pair 2. Definition of linear pair 3. ∠ABD is supplementary to ∠1 ∠ACD is supplementary to ∠2 3. Linear Pair Postulate 4. ∠ABD ≌ ∠ACD 4. Supplements to congruent angles are congruent 5. Given 6. Definition of midpoint 7. ∠ADB is a right angle ∠ADC is a right angle 7. Given 8. ∠ADB ≌ ∠ADC 8. Any two right angles are congruent 9. △ ADB ≌ △ ADC 9. ASA Congruence Postulate D A B C 1 2

15. SSS Congruence Postulate (Side-Side-Side) If three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent. 9/3/20XX Presentation Title 15

16. We can illustrate the congruency of the two triangles using SSS Congruence Postulate by considering and below.   9/3/20XX Presentation Title 16 If (side) (side) (side) Then by SSS Congruence Postulate    

17. In the figure below, corresponding congruent parts are marked to show that the two triangles are congruent by SSS Congruence Postulate. 9/3/20XX Presentation Title 17 Congruent Parts: Then         Congruent Parts: Then        

18. Given: Prove: △ ABC ≌ △ ADC   STATEMENTS REASONS 1. 1. Given 2. 2. Given 3. 3. Reflexive Property 4. △ ABC ≌ △ADC 4. SSS Congruence Postulate STATEMENTS REASONS 1. Given 2. Given 3. Reflexive Property 4. △ ABC ≌ △ADC 4. SSS Congruence Postulate 9/3/20XX Presentation Title 18 B C D A

19. Given: A is the midpoint of Prove: △ JAK ≌ △ NAK   STATEMENTS REASONS 1. 1. Given 2. A is the midpoint of 2. Given 3. 3. Reflexive Property 4. 4. Definition of midpoint 5. △ JAK ≌ △NAK 5. SSS Congruence Postulate STATEMENTS REASONS 1. Given 2. Given 3. Reflexive Property 4. Definition of midpoint 5. △ JAK ≌ △NAK 5. SSS Congruence Postulate 9/3/20XX Presentation Title 19 A K J N

20. SEATWORK 9/3/20XX Presentation Title 20

21. Given : bisects Prove:   Statements Reasons 1. 1. Given 2. bisects 2. 3. 3. Definition of angle bisector 4. 4. Reflexive Property 5. 5. Statements Reasons 1. 1. Given 2. 3. 3. Definition of angle bisector 4. 4. Reflexive Property 5. J E N U Choices Given SAS Congruence Postulate  

22. Agenda Topic one Topic two Topic three Topic four 9/3/20XX Presentation Title 22

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24. Topic one Subtitle

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26. Table Category 1 Category 2 Category 3 Category 4 Item 1 4.5 2.3 1.7 5 Item 2 3.2 5.1 4.4 3 Item 3 2.1 1.7 2.5 2.8 Item 4 4.5 2.2 1.7 7 9/3/20XX Presentation Title 26

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31. Content Subtitle Add text, images, art, and videos. Add transitions, animations, and motion. Save to OneDrive, to get to your presentations from your computer, tablet, or phone. Subtitle Open the Design Ideas pane for instant slide makeovers. When we have design ideas, we’ll show them to you right there. Subtitle This PowerPoint theme uses its own unique set of colors, fonts, and effects to create the overall look and feel of these slides. PowerPoint has tons of themes to give your presentation just the right personality. 9/3/20XX Presentation Title 31

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