1. Classification of Triangles
Geometry Chapter 4 Review
Classification of Triangles
Angles
Sides

2. Geometry Chapter 4 Review
Classify triangles by angles:
1. The measure of two angles are 35 and 55.

3. Geometry Chapter 4 Review
Classify triangles by angles:
1. The measure of two angles are 35 and 55.
2. The measures of two angles are 70 and 50.

4. Geometry Chapter 4 Review
Classify triangles by angles:
1. The measure of two angles are 35 and 55.
2. The measures of two angles are 70 and 50.
3. The measure of one acute angle of a right triangle
is 3/2 the measure of the other acute angle.
Find the measure of each acute angle.

5. Geometry Chapter 4 Review
Classify triangles by angles:
1. The measure of two angles are 35 and 55.
2. The measures of two angles are 70 and 50.
3. The measure of one acute angle of a right triangle
is 3/2 the measure of the other acute angle.
Find the measure of each acute angle. 4.
ABC is isosceles with: AC = AB, AC = 4x - 2
AB = 2x + 6, BC = 3x - 1
Find BC.

6. Geometry Chapter 4 Review
Prove the 180 Theorem

7. Geometry Chapter 4 Review
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONTRUENT.

8. Geometry Chapter 4 Review
EXTERIOR ANGLE Theorem –
The measure of an EXTERIOR Angle of a Triangle
is EQUAL to
the SUM of the Measures
of the TWO REMOTE Interior Angles.

9. Using the figure at the right, answer the following : If m  4 is 140,
Geometry Chapter 4 Review
Using the figure at the right,
answer the following :
If m  4 is 140,
then m  2 = _______

10. Using the figure at the right, answer the following : If m  C = 72,
Geometry Chapter 4 Review
Using the figure at the right,
answer the following :
If m  C = 72,
then the m  1 = ________

11. Using the figure at the right, answer the following : If m  2 = 34,
Geometry Chapter 4 Review
Using the figure at the right,
answer the following :
If m  2 = 34,
then m  4 = __________

12. Geometry Chapter 4 Review
Definition: COROLLARY
A statement that can be easily proved using a theorem
is called a COLOLLARY.
The ACUTE ANGLES of a right triangle
are COMPLEMENTARY.
There can be at most one right or obtuse angle
in a triangle.

13. Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles F C B D E A

14. Congruent TRIANGLES have
Congruent CORRESPONDING SIDES
Congruent CORRESPONDING Angles
The way you NAME the Triangle establishes the
CORRESPONDENCE:

15. SO, if ABC  FGH:
Congruent Angles Congruent Sides
Be sure to WRITE the LETTERS of VERTICES
in the CORRECT ORDER when you write a  Statement.

17. H
Geometry Chapter 4 Review Y T
Given: L G P
Are these Triangles CONGRUENT?

21. To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT
Prove COORESPONDING SIDES are CONGRUENT
(SSS)
Prove Two CORRESPONDING Angles and the
INCLUDED SIDE are CONGRUENT (ASA)
Prove Two CORRESPONDING Sides and the
INCLUDED ANGLE are CONGRUENT (SAS)
Prove Two CORRESPONDING Angles and a
NONIncluded Side are CONGRUENT (AAS)

22. H
Geometry Chapter 4 Review Y T
Given: L G P
Are these Triangles CONGRUENT?

23. H
Geometry Chapter 4 Review Y T
Given: L G P
Are these Triangles CONGRUENT?

24. H
Geometry Chapter 4 Review Y T
Given: L G P
Find:

25. Geometry Chapter 4 Review
Given:
ST = 2x + 13
YZ = 4x + 5
TR = 3x - 1
Find ZX:

26. Geometry Chapter 4 Review
Given: P M T
Prove: Q

29. Triangle MNO is both equilateral and equiangular.
Triangle PQR has 3 congruent sides, m P = 60
and m Q = 60.
Is Triangle MNO  PQR?

32. Geometry Ch 4 Review
CPCTC THEOREM
RECALL:
2 triangles are CONGRUENT, IF:
Their CORRESPONDING Sides are Congruent
AND
Their CORRESPONDING Angles are Congruent.

33. Geometry Ch 4 Review
CPCTC THEOREM
THEREFORE, it follows:
IF --
two triangles can be proved Congruent,
THEN --
Any pair of Corresponding sides or pair of
Corresponding Angles are Congruent.

34. C P C T C Geometry Ch 4 Review CPCTC THEOREM This is abbreviated:
Corresponding Parts of Congruent Triangles
are Congruent.
C P C T C

35. Geometry Chapter 4 ReviewK U G T Y
Given: H
Prove:

37. Geometry Ch 4 Review
Example of CPCTC S R P Q
Given:
Prove:

38. Geometry Ch 4 Review

39. Geometry Ch 4 Review
Another Example of Using CPCTC E 5 6 1 3 4 2 C B F
Given:
Prove:

40. Geometry Ch 4 Review
Yet ANOTHER Example D E C A B
Given:
Prove:

41. Geometry Ch 4 Review
FINAL CPCTC Example A B E C D
Prove:
Given:

42. Geometry Ch 4 Review

43. Geometry Ch 4 Review

44. Geometry Ch 4 Review

45. Geometry Ch 4 Review
Prove:  PWQ   MRQ

46. Geometry Ch 4 Review