GEOMETRY

Chapter 4: 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: (Review) SWBAT: Use triangle classification to find angle measures and side lengths. Pgs: 16-18 Apply theorems about the interior and exterior angles of triangles.

DAY 3: Take Home Quiz: Day 1 to DAY 3

DAY 4: (Ch. 4-3) SWBAT: Use properties of congruent triangles. Pgs: 19-24 Prove triangles congruent by using the definition of congruence. HW: Pgs: 25-27

DAY 5: (Ch. 4-4) SWBAT: Prove triangles congruent by using SSS and SAS. Pgs: 28-33 HW: Pgs: 34-35

DAY 6: (Ch. 4-5) SWBAT: Prove triangles congruent by using ASA and AAS. Pgs: 36-40 HW: Pgs: 41-42

DAY 7: (Ch. 4-5) SWBAT: Prove triangles congruent by using HL. Pgs: 43-46 HW: Page 47

DAY 8: (Review) SWBAT: Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL. Pgs: 48-50

1

Day 1: Triangle Vocabulary and Theorems

Warm – Up

Part I: Vocabulary. Fill out the following chart below.

Example 1:

2

Example 2:

Example 3: Solve for x and y.

Example 4: Solve for x.

3

Algebraic Problems

Example 5:

Example 6:

Example 7:

4

Challenge

Find the measure of the angle indicated.

SUMMARY

5

Exit Ticket

1.

2. Sm,dndnf

6

Day 1: HW

Find the missing angle

7. 8.

9. 10.

7

Find the measure of each angle of the triangle.

11. 12.

13. The angle measures of a triangle are in the ratio of 5:6:7. Find the angle measures of the triangle.

14. The angle measures of a triangle are in the ratio of 10:12:14. Find the angle measures of the triangle.

15. 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.

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. Solve for m

3.

4. Ghfhfh

12

Challenge

Use the information given in the diagram to determine the m .

SUMMARY

2x2+3x-2

4x+3

x2+1

A D

B

C

13

Exit Ticket

Day 2 – HW

14

15

16

Day 3 – Review

8.

17

9.

10.

11.

12.

18

13. If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is….

14.

15. ACD is an exterior angle of ABC, m A = 3x, m ACD = 5x, and m B = 50. What is the value of x?

19

Day 4 – Congruent Triangles

Warm – UP

1.

2.

20

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

21

Ex 2:

In a congruence statement, the order of the vertices indicates the corresponding parts.

Ex 3: If ∆PQR ∆STW, identify all pairs of corresponding congruent parts.

Corresponding Sides Corresponding Angles

22

Example 4:

Example 5:

23

Example 6:

Example 7: ∆ABC ∆DEF

Find the value of x

Find mF.

24

Challenge

SUMMARY

25

Exit Ticket

Day 3 – HW

26

5.

6.

7.

27

8.

9.

10.

11.

28

Day 4 – SSS AND SAS Methods of Proving Triangles Congruent

Warm-Up

Five Ways to Prove Triangles Congruent

In the previous lesson, you learned that congruent triangles have all corresponding sides and all

corresponding angles congruent. Do we need to show all six parts congruent to conclude that two

triangles are congruent?

The answer is no. We can show triangles are congruent by showing few than all three sides and angles

congruent, so long as these congruent sides and angles are in the correct order. The arrangements

that prove triangles congruent are as follows:

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

Hypotenuse-Leg (HL) – for right triangles only

We will take a look at each of these in turn. Today we are going to focus on (SSS) and (SAS).

29

Mark the triangles below to prove the triangles are congruent by the SSS

Theorem.

Example 1:

You Try!

Example 2:

You Try!

G

X

Z

Y

G

X

Z

Y

30

Example 3:

You Try!

a)

b)

31

Mark the triangles below to prove the triangles are congruent by the SAS

Theorem.

Example 4: Given:

Prove: ∆ABC ∆ZXY

Example 5: Given:

Prove:

You Try! Given:

Prove:

32

Example 6:

You

Example 7:

33

Challenge

SUMMARY

34

Exit Ticket

Day 4 – HW

35

36

Day 5 – ASA AND AAS Methods of Proving Triangles Congruent

Warm-Up

For # 1 - 3, state if there is enough information to prove the triangles are congruent. If there is,

state the theorem used and write the congruency statement.

1.

2.

3. f

37

Mark the triangles below to prove the triangles are congruent by the ASA Theorem.

Example 1:

Try It!

Try It!:

38

fjkdfj

39

Mark the triangles below to prove the triangles are congruent by the AAS Theorem.

Example 2:

You Try It!

You Try it!

40

SUMMARY

Exit Ticket

Which method proves why these two triangles are congruent?

41

Day 5 - Homework

42

43

Day 6 – The HL Method of Proving Triangles Congruent

Warm – UP

44

Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell

what other information is needed.

Examples:

_____________________ _____________________

Practice

Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell

what other information is needed.

45

Mark the triangles below to determine whether the HL theorem can be used to prove

triangles congruent.

4.

You Try!

Given: , , and

P Q

R S

46

You Try!

You Try!

Given:

CHALLENGE

SUMMARY

Exit Ticket

47

Day 6 - Homework

48

Day 7 – Review of Congruent Triangles

49

DRAW A PICTURE FOR THIS SECTION! I DREW THE FIRS TWO FOR YOU.

50

Mark the triangles below to prove why the triangles are congruent by the any of the 5 Theorem.

13.

14.

15.

16.

17.