triangles – part 1 introduction to triangles – part 1...

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www.MathNation.com Section 6 Topic 1 Name ____________________________________________ Date_______________ Triangles – Part 1 Introduction to Triangles – Part 1 Independent Practice 1. Consider the diagram below of an equilateral triangle. How long is each side of the triangle? Justify your answer. 2. Match the description to the type of triangle that is produced. Description Type of Triangle a)_______ One Obtuse Angle i. Equilateral b)_______ All 60° angles ii. Acute c)_______ No Congruent sides iii. Obtuse d)_______ One Right Angle iv. Equiangular e)_______ Three Congruent Sides v. Isosceles f)_______ Three Acute Angles vi. Scalene g)_______ Two Congruent Sides vii. Right (7) +10 − 9 4 0 +2 + 15 4 0 1

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Page 1: Triangles – Part 1 Introduction to Triangles – Part 1 ...koltymath.weebly.com/uploads/3/8/1/4/38140883/ip_6.1_and_6.2_1.pdf · Triangles – Part 1 ... Triangles – Part 1 Introduction

www.MathNation.com Section 6 Topic 1

Name ____________________________________________ Date_______________ Triangles – Part 1 Introduction to Triangles – Part 1 Independent Practice 1.   Consider the diagram below of an equilateral triangle.

How long is each side of the triangle? Justify your answer.

2.   Match the description to the type of triangle that is produced.

Description Type of Triangle a)_______  One Obtuse Angle i.   Equilateral

b)_______  All 60° angles ii.   Acute

c)_______  No Congruent sides iii.   Obtuse

d)_______  One Right Angle iv.   Equiangular

e)_______  Three Congruent Sides v.   Isosceles

f)_______   Three Acute Angles vi.   Scalene

g)_______  Two Congruent Sides vii.   Right

(7𝑛)  𝑓𝑡

+10𝑛 −940  𝑓𝑡

+2𝑛 +154 0  𝑓𝑡

1

Page 2: Triangles – Part 1 Introduction to Triangles – Part 1 ...koltymath.weebly.com/uploads/3/8/1/4/38140883/ip_6.1_and_6.2_1.pdf · Triangles – Part 1 ... Triangles – Part 1 Introduction

www.MathNation.com Section 6 Topic 1

3.   Consider the figure below.

Part A: Mrs. Konsdorf claims that angle 𝑅 is a right angle. Is Mrs. Konsdorf correct? Explain your reasoning.

Part B: If 𝑇 is transformed under the rule (𝑥, 𝑦)  →   (𝑥 − 1, 𝑦 − 2), then does 𝑇′ form a right angle

at ∠𝐺𝑅𝑇′?

G

R

T

2

Page 3: Triangles – Part 1 Introduction to Triangles – Part 1 ...koltymath.weebly.com/uploads/3/8/1/4/38140883/ip_6.1_and_6.2_1.pdf · Triangles – Part 1 ... Triangles – Part 1 Introduction

www.MathNation.com Section 6 Topic 1

8

12" #

$ % &

8 3�

4.   Consider the triangle below.

Part A: If Δ𝐴𝑀𝐺 is an isosceles triangle with base 𝐴𝐺, what is the value of 𝑥? Justify your

answer. Part B: What is the length of each leg? Part C: What is the length of the base?

5.   Consider the diagram on the right. Classify each triangle as equilateral, isosceles, or

scalene.

∆𝐼𝐻𝐺: __________________________

∆𝐻𝐽𝐼: __________________________

∆𝐾𝐻𝐼: __________________________

∆𝐻𝐽𝐾: __________________________

M

G A (3𝑥  –0.4)  𝑖𝑛

3

Page 4: Triangles – Part 1 Introduction to Triangles – Part 1 ...koltymath.weebly.com/uploads/3/8/1/4/38140883/ip_6.1_and_6.2_1.pdf · Triangles – Part 1 ... Triangles – Part 1 Introduction

www.MathNation.com Section 6 Topic 2

Name ____________________________________________ Date_______________ Triangles – Part 1 Introduction to Triangles – Part 2 Independent Practice 1.   Consider the figure below.

Determine the measure of each interior angle of △𝑀𝐴𝑁 and classify the triangle.

𝑚∠𝐴 =

𝑚∠𝑀 =

𝑚∠𝑁 =

∆𝑀𝐴𝑁 is a(n) ________________________ triangle.

2.   Triangle 𝐶𝐴𝑇 has vertices at 𝐶(−6, 0), 𝐴(4,−2), and 𝑇(5, 3).

What type of triangle is 𝐶𝐴𝑇?

A  Obtuse B   Isosceles C  Equilateral D  Right

(2𝑥 − 164)°

(𝑥)°  

(𝑥 − 48)° N   A  

M  

4

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www.MathNation.com Section 6 Topic 2

𝑤°

67°

Y

I

K

3.   Garden Plus LLC. Is fencing a triangular garden for Mr. Gold (pictured on the right).

Part A: Determine the expression for the measure of angle 𝑌. Part B: If 𝑚∠𝐼 = 33 and 𝑚∠𝑌 = 14𝑑 − 19, then determine the

value of 𝑑.

4.   Triangle 𝑂𝑀𝐺 has vertices at 𝑂(4,−2), 𝑀(5, 3), and 𝐺(– 6, 0). If point 𝐺 is transformed under

the translation of 𝑥, 𝑦 → (𝑥 + 3, 𝑦 + 2), then △ 𝑂𝑀𝐺′ is

o equilateral.

o isosceles.

o scalene.

5

Page 6: Triangles – Part 1 Introduction to Triangles – Part 1 ...koltymath.weebly.com/uploads/3/8/1/4/38140883/ip_6.1_and_6.2_1.pdf · Triangles – Part 1 ... Triangles – Part 1 Introduction

www.MathNation.com Section 6 Topic 2

5.   Consider the following figure.

Given: ∆𝐴𝐵𝐶,   and 𝐵𝑃 is parallel to 𝐴𝐶. Prove: 𝑚∠1 +𝑚∠2 +𝑚∠3 = 180°

Statements Reasons 1. 𝐴𝐵𝐶 is a triangle. 1.

2. 𝐵𝑃  ||  𝐴𝐶 2.

3.    𝑚∠1 +𝑚∠5 = 𝑚∠𝑃𝐵𝐴 3.

4. 𝑚∠𝑃𝐵𝐴 +𝑚∠4 = 180 4.

5. 𝑚∠1 +𝑚∠5 +𝑚∠4 = 180° 5.

6. ∠2 ≅ ∠4; ∠3 ≅ ∠5 6.

7. 𝑚∠2 = 𝑚∠4; 𝑚∠3 = 𝑚∠5 7.

8. 𝑚∠1 +𝑚∠2 +𝑚∠3 = 180° 8.

A

B

C

P 4 5 1

2 3

6