1. 4.1: Apply Triangle Sum Properties
CHAPTER 4: Congruent Triangles
4.1: Apply Triangle Sum Properties
Aim: To classify triangles and find measures of their angles.
What is a triangle?

2. Classifying Triangles by Sides
Scalene Triangle:
Has no congruent sides.
Isosceles Triangle:
- Has at least two congruent sides.
Equilateral Triangle:
- Has three congruent sides.

3. Classifying Triangles by Angles
Acute Triangle:
- Has three acute angles.
Right Triangle:
- Has one right angle.
Obtuse Triangle:
- Has one obtuse angle.
Equiangular Triangle:
- Has three congruent angles.

4. Graph Triangle ABC Graph A(-5, 4), B(2, 6), and C(4, -1).
Classify the triangle by its sides using the distance formula. B • A • • C
This is an Isosceles triangle.

5. How can we check if any of the angles are right angles?
Using the coordinates A(-5, 4), B(2, 6), and C(4, -1). Find the slope of each line.
What type of triangle is this considered to be?
Right Isosceles Triangle

6. Mini-Activity Move your desk to the person next to you.
Draw 1 straight line (use your ID card for a straight edge).
Take the Triangle give to you and tear off each angle.

7. Theorems Triangle Sum Theorem: Exterior Angle Theorem:
The sum of the measures of the interior angles of a triangle is 180°.
Exterior Angle Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Corollary to the Triangle Sum Theorem:
The acute angles of a right triangle are complementary.

8. CHAPTER 4: Congruent Triangles
4.2: Apply Congruence and Triangles
Date: 11/2
Aim: To identify congruent triangles.
Do Now:
Find m∠ JKM.

9. Write and solve an equation to find the value of x.
Find an angle measure
Find m∠ JKM.
STEP 1
Write and solve an equation to find the value of x.
(2x – 5)° =
70° + x°
Apply the Exterior Angle Theorem.
x = 75
Solve for x.
STEP 2
Substitute 75 for x in 2x – 5 to find m∠ JKM.
2x – 5 = 2 75
– 5 =
145
The measure of ∠ JKM is 145°.
ANSWER

10. Find angle measures from a verbal description
Use the corollary to set up and solve an equation.
x° + 2x° =
90°
Corollary to the Triangle Sum Theorem
x = 30
Solve for x.
So, the measures of the acute angles are 30° and 2(30°)
= 60° .
ANSWER

11. Find the measure of 1 in the diagram shown.
The measure of ∠ 1 in the diagram is 65°.
ANSWER

12. Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

13. CHAPTER 4: Congruent Triangles
4.2: Apply Congruence and Triangles
Date: 11/8/10
Aim: To identify congruent triangles.
Do Now: Take out Homework.

14. CHAPTER 4: Congruent Triangles
4.3: Prove Triangles Congruent by SSS
Date: 11/9/10
Aim: To use the side lengths to prove triangles are congruent.

15. Postulate Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

16. CHAPTER 4: Congruent Triangles
4.4: Prove Triangles Congruent by SAS and HL
Date: 11/10/10
Aim: To use sides and angle lengths to prove congruence.
Do Now:
Page 243 #’s (9 – 14, 20 – 22, 34)

17. Side-Angle-Side Congruence Postulate (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

18. CHAPTER 4: Congruent Triangles
4.4: Prove Triangles Congruent by SAS and HL
Date: 11/12/10
Aim: To use sides and angle lengths to prove congruence.

19. Hypotenuse-Leg Congruence Theorem (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

20. CHAPTER 4: Congruent Triangles
4.5: Prove Triangles Congruent by ASA and AAS
Date: 11/15/10
Aim: To use two more methods to prove congruence (ASA and AAS).

21. Angle-Side-Angle Congruence Postulate (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

22. Angle-Angle-Side Congruence Theorem (AAS)
If two angles and a non-included side of one triangle are congruent to the two angles and the corresponding non-included side of a second triangle, then the two triangle are congruent.

23. 4.6: Use Congruent Triangles
CHAPTER 4: Congruent Triangles
4.6: Use Congruent Triangles
Date: 12/1/09
Aim: To use congruent triangles to prove corresponding parts congruent.

24. 4.6: Use Congruent Triangles
CHAPTER 4: Congruent Triangles
4.6: Use Congruent Triangles
Date: 12/2/09
Aim: To use congruent triangles to prove corresponding parts congruent.

25. 4.7: Use Isosceles and Equilateral Triangles
CHAPTER 4: Congruent Triangles
4.7: Use Isosceles and Equilateral Triangles
Date: 12/3/09
Aim: To use theorems about isosceles and equilateral triangles.

26. Base Angles Theorem
If two sides of a triangle are congruent, then the angels opposite them are congruent.

27. Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.

28. Corollaries Corollary to the Base Angle Theorem:
If a triangle is equilateral, then it is equiangular.
Corollary to the Converse of the Base Angles Theorem:
If a triangle is equiangular, then it is equilateral.