We included **HMH Into Math Grade 4 Answer Key PDF** **Module 17 Lesson 2 Identify and Classify Triangles by Angles **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 17 Lesson 2 Answer Key Identify and Classify Triangles by Angles

I Can measure and classify all of the angles in a triangle.

**Step It Out**

Question 1.

A truss is a triangular framework that supports a roof, a bridge, or other structure. Trusses are engineered to be stable, making them essential for building. How can you identify and classify different triangles?

Answer:

A triangle is a polygon with three sides and three angles.

Identify all of the angles in the triangle. Write whether each angle ¡s right, acute, or obtuse.

∠LMN _________

∠MNL _________

∠ NLM ________

Answer:

∠LMN = **90°**

∠MNL = **45°**

∠ NLM = **45°**

Explanation:

The sum of interior angles of a triangle is equal to 180°.

The angle ∠LMN is equal to 90°. The angle which measures exactly 90 degrees is called as right angle. So, the angle ∠LMN is** right angle**.

The angle ∠MNL is equal to 45°. The angle which measures less than 90 degrees is called as acute angle. So, the angle ∠MNL is **acute angle**.

The angle ∠NLM is equal to 45°. The angle which measures less than 90 degrees is called as acute angle. So, the angle ∠NLM is **acute angle**.

∠QRS ________

∠RSQ ________

∠SQR ________

Answer:

∠QRS = **70°**

∠RSQ = **40°**

∠SQR = **70°**

Explanation:

The sum of interior angles of a triangle is equal to 180°.

The angles ∠QRS and ∠SQR are equal to 70°. The angle which measures less than 90 degrees is called as acute angle. So, the angles ∠QRS and ∠SQR are **acute angles**.

The angle ∠RSQ is equal to 40°. The angle which measures less than 90 degrees is called as acute angle. So, the angle ∠RSQ is **acute angle**.

∠ABC _________

∠BCA ________

∠CAB ________

Answer:

∠ABC = **120°**

∠BCA = **35°**

∠CAB = **25°**

Explanation:

The sum of interior angles of a triangle is equal to 180°.

The angle ∠ABC is equal to 120°. The angle which measures greater than 90 degrees is called as obtuse angle. So, the angle ∠ABC is** obtuse angle**.

The angle ∠BCA is equal to 35°. The angle which measures less than 90 degrees is called as acute angle. So, the angle ∠BCA is **acute angle**.

The angle ∠CAB is equal to 25°. The angle which measures less than 90 degrees is called as acute angle. So, the angle ∠CAB is **acute angle**.

**Turn and Talk** How can you classify each of the triangles now that you have identified all of the angles?

Answer:

A triangle which have one obtuse angle is called as obtuse angled triangle.

A triangle which have one right angle is called as right angled triangle.

A triangle which have three acute angles is called as acute angled angle.

**Step It Out**

Question 2.

You can name a triangle by the vertices of its angles.

A. What are three different ways you can name the triangle in the picture?

Answer:

The above triangle can be named in the following ways.

triangle CAB

triangle ABC

triangle BCA

triangle CBA

triangle BAC

triangle ACB

You can classify triangles into categories by their attributes. One attribute of a triangle is the size of its angles.

B. Classify the triangles. Write the name of the triangle in the correct category. Use a protractor, if needed.

**Connect to Vocabulary**

An acute triangle has three acute angles.

An obtuse triangle has one obtuse angle.

A right triangle has one right angle.

Answer:

**Check Understanding**

**Classify the triangle. Write acute, right, or obtuse. Use a protractor if needed.**

Question 1.

Answer:

It is an obtuse angled triangle as one of the angles of this triangle is greater than 90°.

Explanation:

The angle which measures greater than 90 degrees is called as obtuse angle. The above triangle having one obtuse angle. So, it is called as obtuse angled triangle.

Question 2.

Answer:

It is a right angled triangle as one of the angles of this triangle is equal to 90°.

Explanation:

The angle which measures exactly 90 degrees is called as right angle. The above triangle having one right angle. So, it is called as Right angled triangle.

Question 3.

Answer:

It is an acute angled triangle as all the angles of this triangle are less than 90°.

Explanation:

The angle which measures less than 90 degrees is called as acute angle. The above triangle having three acute angle. So, it is called as acute angled triangle.

**On Your Own**

**Classify the triangle. Write acute, right, or obtuse.**

Question 4.

Answer:

It is an obtuse angled triangle as one of the angles of this triangle is greater than 90°.

Explanation:

The angle which measures greater than 90 degrees is called as obtuse angle. The above triangle having one obtuse angle. So, it is called as obtuse angled triangle.

Question 5.

Answer:

It is an acute angled triangle as all the angles of this triangle are less than 90°.

Explanation:

The angle which measures less than 90 degrees is called as acute angle. The above triangle having three acute angle. So, it is called as acute angled triangle.

Question 6.

Answer:

It is a right angled triangle as one of the angles of this triangle is equal to 90°.

Explanation:

The angle which measures exactly 90 degrees is called as right angle. The above triangle having one right angle. So, it is called as right angled triangle.

Question 7.

Answer:

It is a right angled triangle as one of the angles of this triangle is equal to 90°.

Explanation:

The angle which measures exactly 90 degrees is called as right angle. The above triangle having one right angle. So, it is called as right angled triangle.

Question 8.

Answer:

It is an acute angled triangle as all the angles of this triangle are less than 90°.

Explanation:

The angle which measures less than 90 degrees is called as acute angle. The above triangle having three acute angle. So, it is called as acute angled triangle.

Question 9.

Answer:

It is an obtuse angled triangle as one of the angles of this triangle is greater than 90°.

Explanation:

The angle which measures greater than 90 degrees is called as obtuse angle. The above triangle having one obtuse angle. So, it is called as obtuse angled triangle.

Question 10.

**Reason** Cross out the figure that does not belong. Explain why.

Answer:

Explanation:

From the four triangles given, all are having one angle as right angle except for the second triangle. So, second triangle does not belong with the other triangles.

Question 11.

On figure ABCD, draw a line segment from point A to point C. Name and classify the triangles formed.

Answer:

By drawing a line segment from point A to point C, we will get two triangles ADC and ABC where ADC is a right angled triangle and ABC is an obtuse angled triangle.

Explanation:

From the given fig, we can see that there is a right angle at vertex D. So, the triangle ADC is a right angled triangle.

We can observe that there is an obtuse angle present at vertex B and so the triangle ABC is an obtuse angled triangle.

Question 12.

Use the barn to identify and name triangles. Label the vertices of five triangles. Then classify the triangles as acute, right, or obtuse.

Answer:

Explanation:

By using the barn labeled the vertices of five triangles. All five triangles are Right angled triangle.

Question 13.

**Open Ended** Look around your classroom. Make a list of the triangles that you see. Write acute, right, or obtuse to classify each triangle.

Answer: