1. Chapter 4
Triangle congruency

2. Warm up – Wednesday (GET OUT REVIEW FROM LAST WEEK)
*Test tomorrow on chapter 3*

3. Agenda for week
Wednesday
4.1 and short review
Thursday
TEST ON CHAPTER 3
Friday
4.2 triangle congruency

4. There are two ways to classify triangles
By their angles:
Equilateral – all angles congruent
Acute – all angles are acute
Right – one right angle
Obtuse – one obtuse angle
By their sides
Equilateral – all sides are congruent
Isosceles – two sides are congruent
Scalene – no sides are congruent

5. Classify triangles first by their angles and then by their sides.
2) )
4) )

6. What do the angles in a triangle
add up to?

9. Warm up – Thursday *make sure you have a PENCIL ready for your test*
**If you have any questions about the homework make sure you ask!**

10. Warm up – Friday (have any questions from homework out on your desk!)
*if you haven’t gone up to the board you need to do so! *
Find the value of x for which g || h. Prove your steps.
1) )

11. Review from Wednesday:
**remember the triangle angle sum theorem states that the three angles in a triangle add up to 180 degrees.

12. The variable expressions represent the angle measures of the triangle
The variable expressions represent the angle measures of the triangle. Find the measure of each triangle and then classify the triangle by its angles.
m A = x
m B = 7x
m C = x
m W = 90 degrees
m X = 2x
m Y = x

15. HOMEWORK CHECK! Get out homework from last week and this week!
Last week Wednesday (Pg 149 #33-44 and #1-8 all)
Last week Thursday (Pg 181 #1-16 all)
This week Wednesday (same as Thursday of last week)
This week Thursday (Pg 186 #1-13, 17-22, and all)
** get out piece of paper. NO talking or you will get a zero **

16. Wed night (last week)
#40 #4
#8 show work
Thurs(last week)/Wed(this week) – it was the same thing!
4) #2
5) #9 show work
6) #14
Last nights homework
7) #4
8) #6 show work
9) #19
10) #22 show work

18. Find the value of x, y and z.
Warm up – Tuesday **Homework check this week so ask if you need help**
For Find the measure of the third angle in the triangle given the two angles. Then classify the triangle by its angles.
Find the value of x, y and z.

20. Review from last week:

21. Congruence and triangles
4.2
Congruence and triangles

22. Vocabulary from 4-2
When dealing with CONGRUENT figures you have to identify CORRESPONDING Sides and CORRESPONDING Angles.
Corresponding sides – are a pair of congruent sides in two different figures.
Corresponding angles – are a pair of congruent angles in two different figures.
Congruence statement – stating that two shapes are congruent to each other. MUST PUT THE LETTERS IN THE SAME ORDER!!!

34. Objective check:
3) Find the measure of angle 3 and angle 4.
4) Find the value of x and then find the measure of each angle and classify the triangle. SHOW WORK!

35. Warm up – Friday
Find the measure of each missing angle and classify what type of triangle:
2) 2) 3)
4) Given:
Find 3 pairs of congruent segments
Find 2 pairs of congruent angles.
Challenge: Are they congruent? Justify your answers!
*remember must prove all sides and angles are equal

36. *contest at the end of class if time permits
Today:
*review section 4.2
*start section 4.3
*homework check
*contest at the end of class if time permits

37. Review of 4.2 (practicing justifying your answers)
Are the congruent? If they are congruent, then write a congruency statement.
JUSTIFY YOUR ANSWERS!
1) )

38. Proving triangles congruent by SSS and sas
4.3
Proving triangles congruent by SSS and sas

39. Go to
postulate
section of your
Binder!

40. Ways to prove triangles congruent:

44. Would you use SSS, SAS, or not enough information for either
Would you use SSS, SAS, or not enough information for either? Justify your answers!

45. Classwork:
Page 216
#2-13

46. Practice writing proofs:

47. Warm up – Monday (copy homework and then start warm up)
*Quiz on 4.1 – 4.4 on Thursday – will have proofs on it!*
Find the value of the variables.
1) 2) )
Are the congruent. Explain why or why not!
4) )

48. **Go to postulate/theorem section of your notebook**

50. Warm up – Tuesday (Quiz Thursday!)
A) Name what postulate proves it congruent:
1) 2) 3)
4) )

52. You try:

55. Writing proofs:

59. Warm up – Wednesday (quiz tomorrow)1) 2) 3)

60. *Congruent shapes and corresponding sides and angles
Topics on Quiz
*Congruent shapes and corresponding sides and angles
*Classifying triangles by their angles and sides
*Finding the missing angles of a triangle
*Proofs on SSS, SAS, AAS, and ASA
Remember to study angle pairs because they are
often used in proofs.
**We will review a few problems together and then you
will work on a review on your own.

61. Basic identifications:
State the postulate or theorem that can be used to prove the triangles congruent.
If you cannot prove the triangles congruent, write not enough information.

62. Practicing proofs: try to start it on your own

65. Warm up – Monday (Test on Friday, October 30th )1)

66. Test Friday (you will get your quizzes back today
Test Friday (you will get your quizzes back today. You need to work on proofs before the test because there will be more proofs on the test)
Monday – CPCTC
Tuesday – Practice CPCTC proofs
Wednesday – Hypotenuse/leg theorem
Thursday – review for test
Friday – TEST!

67. Big mistake on your quizzes:
**If you are using SAS, SSS, AAS, or ASA. You must have a PAIR of each of those letters in the acronym in your proof
Ex. If you are proving by AAS…
Your proof must have two pairs of angles and one pair of sides in your proof!!! You cannot assume I know what you mean if it is not on your proof!

68. There will only be one more step to the proof!
You will do the same proofs from last week in order to prove the triangles congruent first.
*SAS, SSS, AAS, ASA*
There will only be one more step to the proof!

69. CPCTC (use the acronym) Corresponding Parts of Congruent Triangles are
New step in the proof – which will be the final step if you are trying to prove a part of a triangle congruent to another part of a triangle.
CPCTC (use the acronym)
Corresponding
Parts of
Congruent
Triangles are

71. Proof 2)

72. Proof 3:

73. You try:
1) )

74. Warm up – Tuesday (test Friday!)
**if you need help on proofs you need to get help during the warm ups
2) )

75. Warm up – Tuesday (test Friday!)
**if you need help on proofs you need to get help during the warm ups
2) )

76. Objective check from yesterday! Look over it with me!
1) )

77. Practice proof together:

78. Warm up – Wednesday (Test Friday!)
**Volunteers to put up the answers today** 1)

79. Topics on test!
Corresponding sides/angles congruent
Exterior angle theorem
Finding the missing angles in a triangle
SSS, SAS, AAS, ASA - proofs
CPCTC – proofs
Hypotenuse-leg theorem
**Remember extra help after school Thursday and any morning for homework questions.

80. Section 4.6 – Proving triangles congruent
Review before section 4.6:
Basics on right triangles:
**remember the
hypotenuse is always
across from the
right angle

81. Review: Basics on isosceles triangles.

85. Equilateral triangle theorems: (you already know this!)

86. Hypotenuse-Leg theorem (HL)
If the hypotenuse and a leg of one right triangle is congruent to the hypotenuse and leg of another right triangle then the triangles are congruent.

87. Practice with all the theorems. If you do not see the parts of the
triangles it is very important that you ask.

92. Using equilateral triangles theorem:
1) )

93. Warm up – Thursday – TEST TOMORROW

95. Using H.L. theorem

97. Make a proof: 3)

98. Find the value of x and y 4)

99. Practice problems of all three:3)
2) )

100. Solve together:
3) Given:
Prove: 2)

101. Extra help!
**Get out your review sheet and a piece of paper.
I am going to go over the ones I think will be the hardest on the test first and then I will review with you whatever you would like to go over.