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

1

Day 1: Sum of Interior Angles of Triangles

Warm – Up

Classifying Triangles by their Sides

2

Practice – Find the missing angle

1) 2) 3)

Algebraic Problems

Practice: Practice:

m 1 = _____

m 2 = _____

m 3 = _____

3

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

4

Challenge

Find the measure of the angle indicated.

SUMMARY

5

Exit Ticket

1.

2.

6

Day 1: HW

7

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

8

Day 2: Exterior Angles of Triangles

Warm - UP

1. Find the measure of the missing angles.

2.

9

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)

10

Part II: Conclusions

1. Investigate the Triangle Sum Theorem and its corollaries

a) 62 + 71 + _____ = _____ (m

b) 23 + 27 + _____ = _____ (m

c) 90 + 37 + _____ = _____ (m

2. Investigate the Exterior Angles Theorem

a) 62 + 71 = _____ m b) 23 + 27 = _____ m c) 37 + ______ = _____ m

(m

What relationship do you notice?

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 ___________

The exterior angle of a triangle is always equal to

Formula: ____ + _____ = ______

11

Part III: Practice. Apply the new theorems to solve each problem

1. Solve for x.

2.

3.

4. Solve for m

12

Challenge

Use the information given in the diagram to

determine the m .

SUMMARY Exit Ticket

2x2+3x-2

4x+3

x2+1

A D

B

C

13

Day 2 – HW

14

15

16

Day 3 – The Isosceles and Equilateral Triangle

Warm – Up Find the measure of the missing angles

17

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.

18

Example 1:

Example 2: Finding the Measure of an Angle

a.

a. 80 b. 55

19

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.

20

Example 5: Finding the Measure of an Angle

Practice Word Problem: Finding the Measure of an Angle

21

Challenge

Find the value of x.

Exit Ticket

1.

2.

22

Day – 3 - Homework

5. 6.

1. 2.

3. 4.

23

11. 12. 13.

24

Day 4 – Constructions

SWBAT: Construct isosceles and equilateral triangles using a compass and a straight edge Warm – Up

25

Student Practice

26

A) B)

27

Challenge Problem

Exit Ticket

28

Homework – Day 4

Construct an isosceles triangle given the length of the base and the length of the sides.

1) 2)

29

3)

4)

30

5)

31

Day 5 – Congruent Triangles

Warm – UP

1.

2.

32

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

33

Ex 2:

Ex 3:

34

Example 4:

Example 5:

35

Example 6:

Example 7: ∆ABC ∆DEF

Find the value of x

Find mF.

36

Challenge

SUMMARY

\\

Exit Ticket

37

Day 5 – HW

38

5.

6.

7.

39

8.

9.

10.

11.

40

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:

_____________________ _____________________

41

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)

_________ ___________

___________ ___________

__________ _________

42

Challenge Problem

Exit Ticket

43

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)____________________

44

13)________________________ 14)____________________ 15)_____________________

16)________________________ 17)____________________ 18)_____________________

19)________________________ 20)____________________ 21)_____________________

22)________________________ 23)____________________ 24)_____________________

45

Day 7 – Review for Test

a. b.

c. d.

46

e.

f.

g.

47

h.

I.

J. In ABC, is extended to D, m B = 2y, m BCA = 6y, and m ACD = 3y. What is m A?

48

K.

L.

M-N.

49

O.

Given:

P.

50

Q. Given:

∆JKM ∆ _______ because of ______.

R.

∆XWZ ∆ _______ because of ______.

S.

51

Determine if you can use SSS, SAS, ASA, and AAS to prove triangles congruent. If not, say no.

Identifying Additional Congruent Parts

A.

B.

C.

D.

a.

b.

c.

d.

T ODA

MODA

OMAN

T OND

T ODA

MN

OA

MA

52

a.

b.

c.

d.

a.

b.

c.

d.

OA

MA

NO

MONA

JC

KE

KAEL

AL

53

3.

4.

54

7. In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB. What is the value of x,

in degrees?

55

Word Problems

1.

2.

3. F 4.

56

CONSTRUCTIONS Construct an isosceles triangle given the length of the base and the length of the sides.

57