﻿ Classifying Triangles Worksheet | Problems & Solutions Classifying Triangles Worksheet

Classifying Triangles Worksheet
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1.
Which of the figures appears to be a right triangle?  a. Figure 2 b. Figure 4 c. Figure 1 d. Figure 3

Solution:

A right triangle has one 90° internal angle (a right angle).

One of the angles in Figure 3 measures 90°.

Figure 3 is a right triangle.

2.
Identify the hypotenuse of the ΔPQR.  a. side PQ b. angle P c. side QR d. angle Q

Solution:

In a right triangle, the side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle.

In the figure, QPR is the right angle.

The side opposite to QPR is QR.

Side QR is the hypotenuse of the ΔPQR.

3.
Which of these is an acute angle in ΔABC?  a. $\angle$BCA b. $\angle$ABC c. $\angle$CBA d. $\angle$ACA

Solution:

ΔABC represents a right triangle with one right angle, ABC and two acute angles, BCA and BAC.

BCA is an acute angle in ΔABC.

4.
Identify the leg(s) in the triangle ABC.  a. AB b. AB, BC c. AB, AC d. AC, BC

Solution:

In the triangle ABC, AC is the hypotenuse.
[The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle.]

AB and BC are the legs of the triangle ABC.
[The other two sides are the legs of the triangle.]

5.
Which of these is the longest side in the right triangle shown?  a. side LM b. side KL c. All sides are equal d. side KM

Solution:

In a right triangle, the side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle.

KLM is the right angle.

The side opposite to KLM is KM.

Side KM is the longest side in the right triangle.

6.
Classify the triangle by the measure of its angles.  a. acute triangle b. straight c. obtuse triangle d. right triangle

Solution:

When one angle of a triangle is greater than 90°, the triangle is called an obtuse angled triangle.

In the figure, one of the angles is 110° which is greater than 90°.

Therefore, the triangle is an obtuse triangle.

7.
A triangle having all its sides of equal length is called an _______ triangle. a. isosceles b. equal c. equilateral d. scalene

Solution:

A triangle having all sides of equal length is known as an equilateral triangle.

8.
A triangle having two sides of equal length is known as an _________ triangle. a. acute angle b. isosceles c. scalene d. equilateral

Solution:

A triangle having two sides of equal lengths is called an isosceles triangle.

9.
A triangle having all its sides of different lengths is known as _______ triangle. a. isosceles b. equilateral c. scalene d. unequal

Solution:

A triangle having all sides of different lengths is known as a scalene triangle. a. obtuse triangle b. straight triangle c. acute triangle d. right triangle