This handy **Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.3 Drawing Geometric Shapes: Triangles** provides detailed answers for the workbook questions

## Spectrum Math Grade 7 Chapter 5 Lesson 5.3 Drawing Geometric Shapes: Triangles Answers Key

When given two angle measures and one side length, a protractor and ruler can be used to create a triangle.

Draw a triangle that has angles of 30° and 80° and a side between them of two inches.

Step 1: Use a ruler to draw a line that is 2 inches.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (30°).

Step 3: Use the protractor to measure the 2^{nd} known angle from the other end of your original line.

Step 4: Label the triangle.

**Use the angles and side lengths given to create triangles. Label the measurements on your drawing.**

Question 1.

a. angles: 50° and 55°

side: 1 inch

Answer:

Explanation:

Step 1: Use a ruler to draw a line that is 1 inch.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (50°).

Step 3: Use the protractor to measure the 2^{nd} known angle from the other end of your original line.

Step 4: Label the triangle.

b. angles: 120° and 30°

side: 2 cm

Answer:

Explanation:

Step 1: Use a ruler to draw a line that is 2 cm.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (30°).

Step 3: Use the protractor to measure the 2^{nd} known angle 120°from the other end of your original line.

Step 4: Label the triangle.

Question 2.

a. angles: 75° and 40°

side: 3 inches

Answer:

Explanation:

Step 1: Use a ruler to draw a line that is 1 inch.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (75°).

Step 3: Use the protractor to measure the 2^{nd} known angle 40° from the other end of your original line.

Step 4: Label the triangle.

b. angles: 60° and 100°

side: 2 inches

Answer:

Explanation:

Step 1: Use a ruler to draw a line that is 2 in.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (60°).

Step 3: Use the protractor to measure the 2^{nd} known angle 100°from the other end of your original line.

Step 4: Label the triangle.

When given the length of two sides and the measure of an angle that is not between the sides, a triangle can be drawn.

Draw a triangle that has sides of 2 inches and 1\(\frac{1}{2}\) inches and a non-included angle of 45°.

Step 1: Draw a line of any length.

Step 2: Use a protractor to draw a 2-inch line that creates the desired angle with the first line (45°).

Step 3: Use a compass set at 1\(\frac{1}{2}\) inches to find where the third line will intersect the base.

Step 4: Label the triangle.

**Use the angles and side lengths given to create triangles. Label the measurements on your drawing.**

Question 1.

a. angle: 50°

sides: 1 inch and 2 inches

Answer:

Explanation:

Draw a triangle that has sides of 1 inch and a non-included angle of 50°.

Step 1: Draw a line of any length.

Step 2: Use a protractor to draw a 1-inch line that creates the desired angle with the first line (50°).

Step 3: Use a compass set at 2 inches to find where the third line will intersect the base.

Step 4: Label the triangle ABC with angle at A.

b. angle: 140°

sides: 3 cm and 4 cm

Answer:

Explanation:

Draw a triangle that has sides of 1 inch and a non-included angle of 140°.

Step 1: Draw a line of any length.

Step 2: Use a protractor to draw a 3-inch line that creates the desired angle with the first line (140°).

Step 3: Use a compass set at 4 inches to find where the third line will intersect the base.

Step 4: Label the triangle ABC with angle at A.

Question 2.

a. angle: 85°

sides: 2 inches and 4 inches

Answer:

Explanation:

Draw a triangle that has sides of 2 inch and a non-included angle of 85°.

Step 1: Draw a line of any length.

Step 2: Use a protractor to draw a 2-inch line that creates the desired angle with the first line (85°).

Step 3: Use a compass set at 4 inches to find where the third line will intersect the base.

Step 4: Label the triangle ABC with angle at A.

b. angle: 100°

sides: 2 cm and 5 cm

Answer:

Explanation:

Draw a triangle that has sides of 2 cm. and a non-included angle of 100°.

Step 1: Draw a line of any length.

Step 2: Use a protractor to draw a 2 cm line that creates the desired angle with the first line (50°).

Step 3: Use a compass set at 5 cm to find where the third line will intersect the base.

Step 4: Label the triangle PQR.

**When given the lengths of three line segments, determine if the segments make a triangle by examining their relationship. Each pair of sides added together must be greater than the remaining side.**

a + b > c

a + c > b

b + c > a

4 + 2 > 3

4 + 3 > 2

3 + 2 > 4

Because the measurements follow the rules, the side lengths make a triangle.

**Using the given lengths, determine if they will make a triangle. Circle yes or no.**

Question 1.

a. Side 1: 5 inches

Side 2: 3 inches

Side 3: 2 inches

yes

no

Answer:

Explanation:

Given a = 5, b = 3, c = 2

a + b > c

a + c > b

b + c > a

5 + 3 not greater then 2

5 + 2 not greater then 3

Because the measurements do not follow the rules, the side lengths can not make a triangle.

b. Side 1: 3 feet

Side 2: 8 feet

Side 3: 7 feet

yes

no

Answer:

Explanation:

Given a = 3, b = 8, c = 7

a + b > c

a + c > b

b + c > a

3 + 8 greater then 7

8 + 7 greater then 3

3 + 7 greater then 8

Because the measurements follow the rules, the side lengths make a triangle.

c. Side 1:10 inches

Side 2: 4 inches

Side 3: 12 inches

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

10 + 4 greater then 12

4 + 10 greater then 12

12 + 10 greater then 4

Because the measurements follow the rules, the side lengths make a triangle.

Question 2.

a. Side 1: 5 centimeters

Side 2: 8 centimeters

Side 3: 20 centimeters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

5 + 8 not greater then 20

8 + 5 not greater then 20

Because the measurements do not follow the rules, the side lengths can not make a triangle.

b. Side 1: 5 meters

Side 2: 9 meters

Side 3: 20 meters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

5 + 9 not greater then 20

9 + 5 not greater then 20

Because the measurements do not follow the rules, the side lengths can not make a triangle.

c. Side 1: 10 inches

Side 2: 10 inches

Side 3: 19 inches

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

10 + 10 greater then 19

10 + 10 greater then 19

10 + 19 greater then 10

Because the measurements follow the rules, the side lengths make a triangle.

Question 3.

a. Side 1: 4 millimeters

Side 2: 9 millimeters

Side 3: 9 millimeters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

9 + 9 greater then 4

9 + 9 greater then 4

4 + 9 greater then 9

Because the measurements follow the rules, the side lengths make a triangle

b. Side 1: 4 inches

Side 2: 4 inches

Side 3: 7 inches

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

4 + 4 greater then 7

4 + 4 greater then 7

4 + 7 greater then 4

Because the measurements follow the rules, the side lengths make a triangle

c. Side 1: 7 centimeters

Side 2: 5 centimeters

Side 3: 14 centimeters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

7 + 5 not greater then 14

5+ 7 not greater then 14

Because the measurements do not follow the rules, the side lengths can not make a triangle.

Question 4.

a. Side 1: 3 centimeters

Side 2: 3 centimeters

Side 3: 10 centimeters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

3 + 3 not greater then 10

3 + 3 not greater then 10

Because the measurements do not follow the rules, the side lengths can not make a triangle.

b. Side 1: 4 yards

Side 2: 8 yards

Side 3: 6 yards

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

4 + 8 greater then 6

8 + 4 greater then 6

8 + 6 greater then 4

Because the measurements follow the rules, the side lengths make a triangle

c. Side 1: 2 meters

Side 2: 3 meters

Side 3: 4 meters

yes

no

Answer:

Explanation:

a + b > c

a + c > b

b + c > a

2+ 4 greater then 3

4 + 2 greater then 3

4 + 3 greater then 2

Because the measurements follow the rules, the side lengths make a triangle