1. Chapter 4: Congruent Triangles
Lesson 1: Classifying Triangles

2. Classifying Triangle by Angles
Acute Triangle: all of the angles are acute
Obtuse Triangle: one angle is obtuse, the other two are acute
Right Triangle: one angle is right, the other two are acute
Equiangular Triangle: all the angles are 60 degrees

3. Classifying Triangles by Sides
Scalene Triangle: all sides are different measures
Isosceles Triangle: at least two sides have the same measure
Equilateral Triangle: all sides have the same measure 7 3 5
* vertex angle= formed by the two congruent sides of an isosceles triangle
* base= the side of an isosceles triangle not congruent to the others

4. If point Y is the midpoint of VX, and WY = 3
If point Y is the midpoint of VX, and WY = 3.0 units, classify ΔVWY as equilateral, isosceles, or scalene. Explain your reasoning.

5. ALGEBRA Find the measure of the sides of isosceles triangle KLM with base KL.__

6. ALGEBRA Find x and the measure of each side of equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and AC = 13 – x.

7. Find the measure of each side of Triangle JKL and classify the triangle based on its sides.

8. Find y
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9. Chapter 4: Congruent Triangles
Lesson 2: Angles of Triangles

10. The acute angles of a right triangle are complementary
The sum of the measures of the angles of a triangle is always 180 degrees.
The acute angles of a right triangle are complementary
There can be at most one right or one obtuse angle in a triangle
Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are also congruent. X A Y B Z C
If A X, and B Y, then
C Z.

11. Interior and Exterior Angles of Triangles
Exterior angle: formed by one side of a triangle and the extension of another side
The interior angles farthest from the exterior angle are its remote interior angles. (remote interior angles are not adjacent to the exterior angle)
Remote interior angles
Exterior angle
An exterior angle is equal to the sum of its remote interior angles.
ex: = 4 2 1 3 4

12. The acute angles of a right triangle are supplementary
Anticipation Guide: read each statement. State whether the sentence is true or false. If the statement is false- rewrite it with the correct term in place of the underlined word
The acute angles of a right triangle are supplementary
The sum of the measures of the angles of any triangle is 100
A triangle can have at most one right angle or acute angle
If two angles of one triangle are congruent to two angles of another triangle, then the third angle of the triangles are congruent
The measure of an exterior angle of a triangle is equal to the difference of the measures of the two remote interior angles
If the measures of two angles of a triangle are 62 and 93, then the measure of the third angle is 35
An exterior angle of a triangle forms a linear pair with an interior angle of the triangle

13. SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle.

14. Find the measure of each numbered angle.

15. GARDENING Find the measure of FLW in the fenced flower garden shown.

16. The piece of quilt fabric is in the shape of a right triangle
The piece of quilt fabric is in the shape of a right triangle. Find the measure of ACD.

17. Find the measure of each numbered angle.

18. Find m3.

19. Chapter 4: Congruent Triangles
Lesson 6: Isosceles Triangles

20. Isosceles Triangles . Vertex Angle
- If two sides of a triangle are congruent, the two angles opposite of them are also congruent
leg
leg
-If two angles of a triangle are congruent, then two sides opposite of them are also congruent
Base angles
- If a triangle is equilateral, it is also equiangular

21. A. Find mR.
B. Find PR

22. A. Find mT.

23. ALGEBRA Find the value of each variable

24. Chapter 4: Congruent Triangles
Lesson 3: Congruent Triangles

25. Definition of Congruent Triangles
Congruent triangles are triangles with exactly the same size and shape
CPCTC: Corresponding Parts of Congruent Triangles are Congruent
Two triangles are congruent if and only if their corresponding parts are congruent

26. Corresponding Parts A
Corresponding parts have the same congruence markings
AB HI
AC HJ
BC IJ
A H
B I
C J B C H I J

27. Congruence Transformations
Slide or Translation: the triangle is in the same position farther down, up, or across the page
Turn or Rotation: the triangle is spun around a point (usually one of the angles)
Flip or reflection: the triangle is shown in a mirror image across a line of symmetry

28. Write a congruence statement for the triangles.

29. Name the corresponding congruent angles for the congruent triangles.

30. In the diagram, ΔITP  ΔNGO. Find the values of x and y.

31. In the diagram, ΔFHJ  ΔHFG. Find the values of x and y.

32. Prove: ΔQNP  ΔOPN Proof: 1. 1. Given 2.
Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof: 1.
1. Given 2.
2. Reflexive Property of Congruence
3. Q  O, NPQ  PNO
3. Given
4. _________________
4. QNP  ONP ?
5. Definition of Congruent Polygons
5. ΔQNP  ΔOPN

33. Write a two-column proof.
Prove: ΔLMN  ΔPON

34. Chapter 4: Congruent Triangles
Lesson 4 and 5: Proving Congruence- SSS, SAS, ASA, AAS, and HL

35. SSS
Side-Side-Side
If all three sets of corresponding sides are congruent, the triangles are congruent A M B C N O
ABC MNO

36. SAS
Side-Angle-Side
If two corresponding sides and the included angles of two triangles are congruent, then the triangles are congruent
* The included angle is the angle between the congruent sides X F Y Z G H
XYZ FGH

37. ASA
Angle-Side-Angle
If two sets of corresponding angles and the included sides are congruent, then the triangles are congruent
* The included side is the side between the two congruent angles J R L K T S
JKL RST

38. AAS
Angle-Angle-Side
If two sets of corresponding angles and one of the corresponding non-included sides are congruent, then the triangles are congruent T E G F V U
EFG
TUV

39. HL
Hypotenuse-Leg
If the hypotenuse and one set of corresponding legs of two right triangles are congruent, then the triangles are congruent C R D H A M
CDH
RAM

40. Determine if the triangles are congruent
Determine if the triangles are congruent. If they are, write the congruence statement.

41. Given: AC  AB D is the midpoint of BC. Prove: ΔADC  ΔADB
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42. Determine whether ΔABC  ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).

43. Determine if the triangles are congruent
Determine if the triangles are congruent. If they are, write the congruence statement.

44. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

45. Write a two column proof.