1. Chapter 4- Part 2
Congruent Triangles

2. CPCTC (4-4) Definition of Congruent Triangles Corresponding Parts of
Triangles are

3. Using Congruent Triangles: CPCTC
CPCTC – Corresponding parts of congruent triangles are congruent.
DEF ≅ DGF by _____
What other parts are congruent by CPCTC?

4. Using Congruent Triangles: CPCTC
ACE ≅ BDE by _________ What other parts are congruent by CPCTC?

5. Class work
4-3 Part 1 worksheet (complete in groups)

6. Homework
4-4 Practice worksheet #1-5

7. Homework
p #6, 7, 9, 10, and 16 (proofs using CPCTC)

8. Triangle Paper Activity (5 minutes!)
Fold paper in half and crease the fold
Cut off a corner (not on the creased side) to make a triangle.
Open the triangle and lay it flat.
Label the triangle vertices P, R, and S and the bottom of the fold Q.
Measure the lengths of the sides of the triangle using a ruler and measure the angles using a protractor. Record your measurements on the triangle.
Compare the lengths of the sides and the angle measures. Identify angle pairs and side pairs that are congruent.
Write a conjecture (if… then…) regarding your findings.

9. Isosceles Triangles (4-5)
Parts of an Isosceles Triangle
Base
Legs
Vertex Angle
Base Angles

10. Isosceles Triangles (4-5)
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

11. Triangle Paper Activity
Using the same triangle as previously,
Draw a line down the crease of the triangle.
Measure <PRQ and <SRQ. Compare these measurements.
Measure <PQR and <SQR. Compare these measurements.
Find PQ and QS using a ruler.
Compare these two angle pairs and lengths of sides with other students’ pairs of angles and lengths of sides. Do you notice a pattern?
Write a conjecture (conclusion based on observations). Write your conjecture as an “if-then” conditional statement.

12. Isosceles Triangles (4-5)
Corollary:
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
In other words, the bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

13. Isosceles Triangles (4-4)
Find the values of x and y.

14. Equilateral Triangles (4-5)
Corollaries involving equilateral triangles:
If a triangle is equilateral, then the triangle is equiangular.
If a triangle is equiangular, then the triangle is equilateral.

15. Classwork
4-4 Handout (part 1)

16. Homework
Isosceles and Equilateral Triangles worksheet

17. Right Triangle Congruence (4-6)
Hypotenuse-Leg (HL) Theorem
If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

18. Summary of Ways to Prove Two Triangles are Congruent
All triangles
SSS
SAS
ASA
AAS
Right Triangles
All ways listed above HL

19. Example

20. Class work Right Triangle Congruence worksheet
Review answers in ~15 minutes!

21. Homework
4-5 Other Methods of Proving Triangles Congruent worksheet (1-5 all)

22. Section 4-7 Using More Than One Pair of Congruent Triangles
Given: ∠1 ≅∠2; ∠3 ≅∠4
Prove: TU ≅ TW
How many triangles do you see here?
Which two triangles can we first prove are congruent?

23. Statements Reasons
1. ∠1≅∠2; ∠3≅∠4 Given
2. 𝑆𝑉≅𝑆𝑉 Reflexive
3. ⊿𝑈𝑆𝑉≅⊿𝑊𝑆𝑉 ASA
4. 𝑈𝑉≅𝑊𝑉 CPCTC
5. 𝑇𝑉≅𝑇𝑉 Reflexive
6. ⊿𝑇𝑈𝑉≅⊿𝑇𝑊𝑉 SAS
7. 𝑇𝑈≅𝑇𝑊 CPCTC