Geometry Regents: Unit 5 Triangles
Name:______
Teacher:______
Pd: ______
Table of Contents
DAY 1: (Ch. 4-1 & 4-2) SWBAT: Classify triangles by their angle measures and side lengths. Pgs: 1-5 Use triangle classification to find angle measures and side lengths. Pgs: 6-7
DAY 2: (Ch. 4-2) SWBAT: Apply theorems about the interior and exterior angles of triangles. Pgs: 8-12 HW: Pgs: 13-15
DAY 3: (Ch. 4-8) SWBAT: Apply Properties of Equilateral and Isosceles Triangles. Pgs: 16-21 HW: Pgs: 22-23
DAY 4: SWBAT: Construct isosceles and equilateral triangles using a compass and a straight edge Pgs: 24-27 HW: Pgs: 28-30
DAY 5: (Ch. 4-3) SWBAT: Use properties of congruent triangles to solve for missing sides and/or angles Pgs: 31-36 Prove triangles congruent by using the definition of congruence. HW: Pgs: 37-39
DAY 6: (Ch. 4-4 to 4-5) SWBAT: Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL. Pgs: 40-42 HW: Pgs: 43-44
REVIEW Pgs: 45-56
Day 1: Sum of Interior Angles of Triangles
Warm – Up
Classifying Triangles by their Sides
1
m 1 = _____
m 2 = _____
m 3 = _____
Practice – Find the missing angle 1) 2) 3)
Algebraic Problems
Practice: Practice:
2
Example 3:
Example 4: The ratio of the measures of the angles of a triangle is 4:5:6. Find the measure of the angles and classify the triangle as acute, right, or obtuse.
Practice:
Practice
Practice
3
Challenge
Find the measure of the angle indicated.
SUMMARY
4
Exit Ticket
1.
2.
5
Day 1: HW
6
13. The angle measures of a triangle are in the ratio of 5:6:7. Find the angle measures of the triangle.
14.
15.
16. If the measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x − 6, the triangle must be:
1) Isosceles 2) Equilateral 3) Right 4) Scalene
7
Day 2: Exterior Angles of Triangles
Warm - UP
1. Find the measure of the missing angles.
2.
8
Part I: Angle relationships in triangles. Find the measure of all angles in the triangles below. Then answer the following questions and try to develop the theorems that represent these relationships. After checking the theorems with your teacher, then complete the remaining examples. a)
b)
c)
9
Part II: Conclusions
1. Investigate the Triangle Sum Theorem and its corollaries
a) 62 + 71 + _____ = _____ (m
b) 23 + 27 + _____ = _____ (m
c) 90 + 37 + _____ = _____ (m
In any triangle, the sum of the interior angles is equal to ______
In a right triangle, the two acute angles are ______.
In an equiangular triangle, all angles measure ______
2. Investigate the Exterior Angles Theorem
a) 62 + 71 = _____ m
b) 23 + 27 = _____ m
c) 37 + ______ = _____ m (m
What relationship do you notice?
The exterior angle of a triangle is always equal to
Formula: ____ + _____ = ______
10
Part III: Practice. Apply the new theorems to solve each problem
1. Solve for x.
2.
3.
4. Solve for m
11
B Challenge 4x+3 Use the information given in the diagram to determine the m . x2+1 2x2+3x-2 A C D
SUMMARY
Exit Ticket
12
Day 2 – HW
13
14
15
Day 3 – The Isosceles and Equilateral Triangle
Warm – Up Find the measure of the missing angles
16
If all the angles are congruent in a triangle, then the measure of each angle is ______.
Example 1 – Find the value of x
Practice:
2. Find the value of OP.
17
Example 1:
Example 2: Finding the Measure of an Angle
a. a. 80 b. 55
18
Example 3:
a. 40 b. 150
Example 4: Finding the Measure of an Angle Find mG.
Practice: Finding the Measure of an Angle
Find mN.
19
Example 5: Finding the Measure of an Angle
Practice Word Problem: Finding the Measure of an Angle
20
Challenge Find the value of x.
Exit Ticket 1.
2.
21
Day – 3 - Homework
1. 2.
3. 4.
5. 6.
22
11.
12.
13.
23
Day 4 – Constructions
SWBAT: Construct isosceles and equilateral triangles using a compass and a straight edge
Warm – Up
24
Student Practice
25
A) B)
26
Challenge Problem
Exit Ticket
27
Homework – Day 4
Construct an isosceles triangle given the length of the base and the length of the sides.
1)
2)
28
3)
4)
29
5)
30
Day 5 – Congruent Triangles
Warm – UP
1.
2.
31
Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same ______in polygons with an equal number of ______.
Two polygons are ______polygons if and only if their ______sides are ______. Thus triangles that are the same size and shape are congruent.
Ex 1: Name all the corresponding sides and angles below if
Corresponding Sides Corresponding Angles
32
Ex 2:
Ex 3:
33
Example 4:
Example 5:
34
Example 6:
Example 7: ∆ABC ∆DEF
Find the value of x
Find mF.
35
Challenge
SUMMARY
\\
Exit Ticket
36
Day 5 – HW
37
5.
6.
7.
38
8.
9.
10.
11.
39
Day 6 – Proving Triangles Congruent
DO NOW
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent.
Example 1:
______
40
Practice
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent. a) b) c)
d) e) f)
______
______
______41
Challenge Problem
Exit Ticket
42
HOMEWORK
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent.
1)______2)______3)______
4)______5)______6)______
7)______8)______9)______
10)______11)______12)______43
13)______14)______15)______
16)______17)______18)______
19)______20)______21)______
22)______23)______24)______
44
Day 7 – Review for Test
a. b.
c. d.
45
e.
f.
g.
46
h.
I.
J. In ABC, is extended to D, m B = 2y, m BCA = 6y, and m ACD = 3y. What is m A?
47
K.
L.
M-N.
48
O.
Given: ̅̅̅ ̅ ̅ ̅̅̅ ̅
̅̅̅ ̅ ̅̅̅ ̅
P.
49
Q. Given:
∆JKM ∆ ______because of ______.
R.
∆XWZ ∆ ______because of ______.
S.
50
Determine if you can use SSS, SAS, ASA, and AAS to prove triangles congruent. If not, say no.
Identifying Additional Congruent Parts
A. AN OM B. DA MO
C. ND TO
D. DA TO
a. A O b. N M c. DA TO d. A M
51
a. O N b. A M c. A O d. NA MO
a. EL KA b. C J c. E K d. L A
52
3.
4.
53
7. In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB. What is the value of x, in degrees?
54
Word Problems
1.
2.
3. F
4.
55
CONSTRUCTIONS Construct an isosceles triangle given the length of the base and the length of the sides.
56
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