We included **HMH Into Math Grade 7 Answer Key PDF** **Module 9 Lesson 3 Draw and Construct Triangles Given Angle Measures **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 9 Lesson 3 Answer Key Draw and Construct Triangles Given Angle Measures

I Can determine whether it is possible to draw a triangle with three given angle measures. If it is, I can construct such a triangle.

**Spark Your Learning**

A town is designing triangular flower beds for a park. Is it possible to choose three angle measures that will not form a triangle? If so, draw several examples.

Answer:

90°, 90°, 90° is not possible to choose three angle measures that will not form a triangle.

Explanation:

Sum of the three angles in triangle is 180 degrees.

So, if three angles are of 90 degrees than the sum is 90 + 90 + 90 = 240 degrees.

**Turn and Talk** Pick one of your examples above and describe how you could revise your drawing to form a triangle.

Answer:

60°, 60° and 60° three angle measures that can form a triangle

Explanation:

Sum of the three angles in triangle is 180 degrees.

So, 60 + 60 60 = 180

**Build Understanding**

Question 1.

Antonio and Karen are making quilts. They are cutting triangle shapes for their quilt. The triangles have angle measures of 45°, 45°, and 90°. The pattern for the triangles Karen is using is shown.

A. Antonio wants his triangles to be larger than Karen’s. Is it possible for Antonio to make larger triangles with the same angle measures? If so, draw sample triangles. If not, explain why he cannot.

Answer:

yes, possible.

Explanation:

It is possible for Antonio to make larger triangles with the same angle measures by increasing the lengths of the sides of the triangles as shown above.

B. Amie is given three angle measures that form a triangle. How many different triangles can Amie make, one or more than one? Explain.

Answer:

Only one triangle can be formed.

Explanation:

As, Amie is given only three angle measures.

So, she can make only one triangle, because the sum of the three angles is 180 degrees.

C. Jess is given three segments that form a triangle. How many different triangles can Jess make, one or more than one? Explain.

Answer:

Unique triangles can be constructed using the same three segments.

Explanation:

As, Jess is given three segments to form a triangle.

She can construct unique triangles with the help of three line segments because line segments are different from the angles.

**Turn and Talk** Is there a maximum number of different triangles that can be made given three angle measures? Explain.

Answer:

No, different angles cannot be formed.

Explanation:

As, we know that the sum of the three triangles is 180 degrees.

So, maximum number of different triangles cannot be formed.

Question 2.

You can use tools to determine whether you can construct a triangle with three given angle measures.

A. Is it possible to construct a triangle with angle measures of 25°, 75°, and 80°? If so, draw the triangle.

Answer:

Yes, it is possible.

Explanation:

The sum of the internal angles of a triangle is 180°

25°, 75°, and 80°

25 + 75 + 80 = 180°

B. Is it possible to construct a triangle with angle measures of 35°, 70°, and 90°? If so, draw the triangle.

Answer:

No, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

35°, 70°, and 90°

35 + 70 + 90 = 195°

A triangle with angle measures of 35°, 70°, and 90° is not possible.

C. Is it possible to construct a triangle with angle measures of 45°, 60°, and 55°? If so, draw the triangle.

Answer:

No, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

45°, 60°, and 55°

45 + 60 + 55 = 160°

a triangle with angle measures of 45°, 60°, and 55° is not possible

D. Find the sum of the angle measures in Parts A – C. For the sets of angles that do not form triangles, what do their sums have in common?

Answer:

No, it is not possible.

Explanation:

The sums of given angles are not equal to 180°

Triangle A

25 + 75 + 80 = 180°

Triangle B

35 + 70 + 90 = 195°

Triangle C

45 + 60 + 55 = 160°

the sets of angles that do not form triangles, what do their sums have in common is not equal to 180°

**Step It Out**

Question 3.

Jenny draws a triangle that includes one angle that has a measure of 30°, one angle that has a measure of 90°, and one side that has a length of 1 inch. Without seeing her triangle, can you draw it?

A. Can the 1-inch side of Jenny’s triangle be a side of both the 30° and 90° angles of the triangle? Can it be a side of only one of the angles?

Answer:

NO, it is not the side of the angle.

Explanation:

Triangle be a side of both the 30° and 90° angles of the triangle

the sum of the two given angles = 30° + 90° = 120°

the sum of three angles is 180°

180° – 120° = 60°

the third angle is 60°

The lengths of the sides will vary by the angle

B. Think about how the given side and the given angles might be positioned. Draw all the triangles you can using the information given for Jenny’s triangle. Label the known measures on your drawings.

Answer:

Explanation:

Jenny can draw only one triangle from the given information.

As, the sum of the angles of a triangle is 180 degrees.

C. Can Jenny’s triangle be found among your drawings? Explain.

Answer:

Yes, we can find her triangle

D. Can you draw a triangle with one 90° angle and one 100° angle so that the side between the angles is 2 inches long? Why or why not?

Answer:

NO, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

90° and 100° = 190°

a triangle with angle measures of 90°, 100°, and x° is not possible

**Check Understanding**

Question 1.

Cliff wants to draw a triangle with a 300 angle and a 60° angle so that the side between them is 2 inches long. How many triangles can he draw?

Answer:

NO, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

300° and 60° = 360°

a triangle with angle measures of 60°, 300°, and x° is not possible

Question 2.

A. If possible, construct a triangle with angle measures of 45°, 65°, and 70°.

Answer:

Yes, it possible to construct a triangle.

Explanation:

As, the sums of given angles are equal to 180°

Triangle

45 + 65 + 70 = 180°

B. How many triangles are possible, none, one, or many?

Answer:

Only one triangle is possible.

Explanation:

As, the sum of the internal angles in a triangle is 180 degrees.

**On Your Own**

Question 3.

Kara is making a picture out of tiles. One tile will be triangular with angle measures of 25°, 25°, and 130°.

A. Use Tools Sketch a triangle with those angle measures.

Answer:

Explanation:

As, the sum of the internal angles in a triangle is 180 degrees.

25° + 25° + 130° = 180°

B. Do you have enough information to make Kara’s triangle? Explain.

Answer:

No, information to make triangle is not enough.

Explanation:

only internal angles of a triangle is given,

but tile size information is needed to make a triangle.

**Use Tools** For Problems 4-7, determine whether it is possible to draw a triangle with the given angle measures. If it is possible, use tools to draw the triangle.

Question 4.

55°, 60°, 70°

Answer:

No, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

55°, 60°, and 70°

55 + 60 + 70 = 185°

a triangle with angle measures of 55°, 60°, and 75° is not possible

Question 5.

30°, 40° 110°

Answer:

Yes, it is possible.

Explanation:

The sum of the internal angles of a triangle is 180°

30°, 40°, and 110°

30 + 40 + 110 = 180°

a triangle with angle measures of 30°, 40°, and 110° is possible

Question 6.

45°, 65°, 70°

Answer:

Yes, it is possible.

Explanation:

The sum of the internal angles of a triangle is 180°

45°, 65°, and 70°

45 + 65 + 70 = 180°

a triangle with angle measures of 45°, 65°, and 70° is possible

Question 7.

25°, 85°, 75°

Answer:

No, it is not possible.

Explanation:

The sum of the internal angles of a triangle is 180°

25°, 85°, and 75°

25 + 85 + 75 = 185°

a triangle with angle measures of 25°, 85°, and 75° is not possible

Question 8.

Use Tools Maurice is making blocks for a children’s toy set. The instructions call for triangles with angle measures of 60°, 60°, and 60°. Draw a triangle with these angle measures.

Answer:

Explanation:

The sum of the internal angles of a triangle is 180°

60° + 60° + 60° = 180°

Question 9.

**Use Tools** Kate is drawing a house. For the top of the house, she wants to make a triangle with angle measures of 30°, 30°, and 120°. Can Kate form a triangle with these angle measures? If so, use tools to draw the triangle. If not, explain why not.

Answer:

Explanation:

The sum of the internal angles of a triangle is 180°

30°, 30°, and 120°

30 + 30 + 120 = 180°

a triangle with angle measures of 30°, 30°, and 120° is possible

Question 10.

**STEM** An engineer is designing a building that is shaped like a triangle and wants to know whether the angles of the triangle can be 50°, 50°, and 70°. Can these be the angles of the triangle? Use tools to draw a diagram that supports your answer.

Answer:

A triangle with angle measures of 50°, 50°, and 70° is not possible

Explanation:

The sum of the internal angles of a triangle is 180°

50°, 50°, and 70°

50 + 50 + 70 = 170°

a triangle with angle measures of 50°, 50°, and 70° is not possible

Question 11.

**Open-Ended** Eduardo is building a triangular sandbox for a playground. He wants the triangle to include a 65° angle, a 50° angle, and at least one side that is 12 feet long. Draw at least one possible triangle on a separate piece of paper and estimate possible lengths of the other two sides of the triangle.

Answer:

Explanation:

The possible lengths of a triangle ABC

b = 12 ft

a + c should be greater then b =12 ft as shown in the above figure.

**I’m in a Learning Mindset!**

How effective were the tools I used to construct triangles? How did I apply my knowledge of properties of triangles to the task?

Answer:

Properties of triangles are very important, which are use full in construction of a triangle.

**Lesson 9.3 More Practice/Homework**

Question 1.

**Use Tools** Vanessa wants to build a triangular table. Can she build a table with angle measures of 15°, 55°, and 110°? If so, draw the triangle.

Answer:

Yes, she can build a triangle.

Explanation:

The sum of the internal angles of a triangle is 180°

15°, 55°, and 110°

15 + 55 + 110 = 180°

a triangle with angle measures of 15°, 55°, and 180° is possible

Question 2.

**Use Tools** Carlos wants to draw a triangle with angle measures of 55°, 60°, and 65°. How many different triangles can Carlos draw: one or more than one?

Answer:

More than one triangle with angles changing their location as shown below,

Explanation:

The sum of the internal angles of a triangle is 180°

65°, 55°, 60° = 180°

**Use Tool** For Problems 3-6, determine whether it is possible to draw a triangle with the given angle measures. If it is possible, use tools to draw the triangle.

Question 3.

25°, 40°, 115°

Answer:

A triangle with angle measures of 25°, 40°, 115° is possible.

Explanation:

The sum of the internal angles of a triangle is 180°

25°, 40°, and 115°

25 + 40 + 115 = 180°

a triangle with angle measures of 25°, 40°, 115° is possible

Question 4.

15°, 15°, 120°

Answer:

A triangle with angle measures of 15°, 15°, 120° is not possible

Explanation:

The sum of the internal angles of a triangle is 180°

15°, 15°, and 120°

15 + 15 + 120 = 150°

a triangle with angle measures of 15°, 15°, 120° is not possible

Question 5.

60°, 70°, 70°

Answer:

A triangle with angle measures of 60°, 70°, 70° is not possible

Explanation:

The sum of the internal angles of a triangle is 180°

60°, 70°, and 70°

60°+ 70°+ 70° = 200°

a triangle with angle measures of 60°, 70°, 70° is not possible

Question 6.

30°, 55°, 95°

Answer:

A triangle with angle measures of 30°, 55°, 95° is possible

Explanation:

The sum of the internal angles of a triangle is 180°

30°, 55°, 95°

30°+ 55°+ 95° = 180°

a triangle with angle measures of 30°, 55°, 95° is possible

Question 7.

**Construct Arguments** James sees a floor made of triangular tiles of different sizes. He notices that two triangles each have one angle with a measure of 35°, another with a measure of 45°, and one side with a length of 6 inches. Are the two triangles the same? Explain.

Answer:

Yes, two triangles are same as shown below,

Explanation:

The sum of the internal angles of a triangle is 180°

180 – 35 + 45 = 100

So, the third angle is 100 degrees.

The sum of the two sides of a triangle is greater than the third side.

6 + 5 = 11

So, the third side is less than 11.

**Test Prep**

Question 8.

How many different triangles can be made with the angle measures 30°, 60°, and 90°?

(A) none

(B) one

(C) exactly two

(D) more than two

Answer:

Option(B)

Explanation:

one triangle (right angle triangle)

can be made with the angle measures 30°, 60°, and 90°

Question 9.

Each set of angle measures and/or side lengths can be used to form a triangle. Which conditions produce only one triangle? Choose all that apply.

(A) 35° angle, 55° angle, 90° angle

(B) 3-inch side, 4-inch side, 5-inch side

(C) 30° angle, 60° angle, 2-inch side joining the angles

(D) 28° angle, 80° angle, 1-meter side

(E) three 60° angles, three \(\frac{3}{4}\)-inch sides

Answer:

(A) 35° angle, 55° angle, 90° angle

(B) 3-inch side, 4-inch side, 5-inch side

(E)three 60° angles, three \(\frac{3}{4}\)-inch sides

Explanation:

The sum of internal angles in triangle is 180 degrees.

35°+ 55°+ 90° = 180°

Question 10.

Seamus draws a triangle with angles of measures 40°, 60°, and 80°. Edwina draws a triangle with these same three angle measures. Which statement must be true?

(A) Edwina’s triangle is the same size as Seamus’s triangle.

(B) Edwina’s triangle is the same shape as Seamus’s triangle.

(C) The perimeter of Seamus’s triangle is greater than the perimeter of Edwina’s triangle.

(D) The area of Edwina’s triangle is less than the area of Seamus.’s triangle.

Answer:

statement must be true

(A) Edwina’s triangle is the same size as Seamus’s triangle.

(B) Edwina’s triangle is the same shape as Seamus’s triangle.

Explanation:

The sum of internal angles in triangle is 180 degrees.

40°+ 60°+ 80° = 180°

**Spiral Review**

Question 11.

Hayden will attend a craft show. The cost of an admission ticket is $8. The cost of a raffle ticket for a handmade quilt (available only to those with an admission ticket) is $5. Hayden has $45. What is the greatest number of raffle tickets he can buy?

Answer:

The greatest number of raffle tickets he can buy is 7

Explanation:

The cost of an admission ticket is $8

The cost of a raffle ticket for a handmade quilt is $5

45 – 8 = 37

37/5 =7.4

the greatest number of raffle tickets he can buy is 7

Question 12.

Find the value of x.

Answer:

18.57°

Explanation:

7x – 5 + 45 = 180

7x – 5 = 180 – 45

7x – 5 = 135

7x = 135 – 5

7x = 130

x = 130/7 = 18.57°