1. 4-5 Warm Up Lesson Presentation Lesson Quiz
Triangle Congruence: ASA, AAS, and HL
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz

2. 4.5 Congruent Triangles by HL
Warm Up
1. What are sides AC and BC called? Side AB?
2. Which side is in between A and C?
3. Given DEF and GHI, if D  G and E  H, why is F  I?
legs; hypotenuse AC
Third s Thm.

3. Objectives 4.5 Congruent Triangles by HL
Apply HL to construct triangles and to solve problems.
Prove triangles congruent by using HL.

4. 4.5 Congruent Triangles by HL
Vocabulary
included side

5. 4.5 Congruent Triangles by HL

6. Example 1: Applying HL Congruence
4.5 Congruent Triangles by HL
Example 1: Applying HL Congruence
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.
According to the diagram, the triangles are right triangles that share one leg.
It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.

7. Example 2: Applying HL Congruence
4.5 Congruent Triangles by HL
Example 2: Applying HL Congruence
This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.

8. 4.5 Congruent Triangles by HL
Check It Out! Example 3
Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If there is, provide a paragraph and two column proof. If not, tell what else you need to know.
Yes; it is given that AC  DB. BC  CB by the Reflexive Property of Congruence. Since ABC and DCB are right angles, ABC and DCB are right triangles. ABC  DCB by HL.

9. 4.5 Congruent Triangles by HL
Check It Out! Example 3 Continue
4. ABC  DCB
4. By HL
3. Reflexive Prop. Leg
3. CB  BC
2. Given Hypotenuse
2. AC  DB.
1. Given Right Angle
1. ABC  DCB
Reasons
Statements

10. 4.5 Congruent Triangles by HL
Lesson Quiz: Part I
Identify the postulate or theorem that proves the triangles congruent and create a two column proof. A HL B C D

11. 4.5 Congruent Triangles by HL A
Lesson Quiz: Part I Continued C B D
4. ADC  ADB
4. By HL
3. Given Leg
3. CD  BD
2. Given Hypotenuse
2. AB  AC.
1. Given Right Angle
1. ADB  ADC
Reasons
Statements

12. 4.5 Congruent Triangles by HL
Lesson Quiz: Part II
Identify the postulate or theorem that proves the triangles congruent and create a two column proof. A HL B C D

13. 4.5 Congruent Triangles by HL A
Lesson Quiz: Part Ii Continued C B D
4. ADC  ADB
4. By HL
3. Given Leg
3. CD  BD
2. Given Hypotenuse
2. AB  AC.
1. Given Right Angle
1. ADB  ADC
Reasons
Statements