﻿ Triangle Worksheets | Problems & Solutions # Triangle Worksheets

Triangle Worksheets
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1.
Identify the type of ΔABC based on its angle measures.  a. Obtuse triangle b. Right triangle c. Equilateral triangle d. None of the above

#### Solution:

In ΔABC, A and B are acute angles and C is an obtuse angle.

A triangle in which one of the angles is obtuse is known as an obtuse triangle.

So, ΔABC is an obtuse triangle.

2.
Can an equilateral triangle be a right triangle? a. No b. Yes

#### Solution:

In an equilateral triangle, each angle is 60o.

In a right triangle, one of the angles must be 90o.

So, an equilateral triangle cannot be a right triangle.

3.
Can a scalene triangle have an acute angle? a. Yes b. No

#### Solution:

In any triangle, atleast two of the angles are acute.

A scalene triangle will have an acute angle.

4.
Find the measure of $\angle$A, if $\angle$C = 59° and $\angle$B = 63°.  a. 43° b. 58° c. 46° d. 70°

#### Solution:

The sum of three angles in a triangle is 180°.

A + B + C = 180°.

A + 63° + 59° = 180°
[Substitute B = 63° and C = 59°.]

A + 122° = 180°
[Combine like terms.]

A = 180° - 122°
[Subtract 122° from both sides.]

A = 58°

5.
Name the right triangles in the rhombus.

(1) ΔABD and ΔBDC
(2) ΔAOD and ΔAOB
(3) ΔBOC and ΔDOC  a. (1) only b. (2) only c. Both (1) and (2) d. Both (2) and (3)

#### Solution:

A triangle is said to be a right triangle, if one of the angles in the triangle is equal to 90o.

In the rhombus, there are four right triangles namely ΔAOD, ΔAOB, ΔBOC and ΔDOC.

So, both (2) and (3) are correct.

6.
Classify the triangles in the figure based on the measure of the angles.  a. Both are obtuse triangles b. ΔPQR is a right triangle and ΔRST is an obtuse triangle c. Both are right triangles d. ΔPQR is an obtuse triangle and ΔRST is a right triangle

#### Solution:

ΔRST has a right angle. So, ΔRST is a right triangle.

ΔPQR has one obtuse angle. So, ΔPQR is an obtuse triangle.

In the figure, ΔPQR is an obtuse triangle and ΔRST is a right triangle.

7.
Find $\angle$A and $\angle$B for the triangle ABC, if $\angle$C = 32°.  a. 74° b. 94° c. 106° d. 84°

#### Solution:

From the figure, AC = BC.

So, ΔABC is isosceles and A = B.

Let A = B = x

In a triangle, the sum of all the angles is equal to 180°.

A + B + C =180°

x + x + 32° = 180°
[Substitute A = B = x and C = 32°.]

2x = 180° - 32°
[Subtract 32° from each side.]

2x = 148°

x = 148°2
[Divide each side by 2.]

x = 74°

8.
ΔABC is an isosceles triangle and $\angle$A = 50°. Which of the following cannot be the measures of other two angles? a. 50°, 80° b. 60°, 80° c. 65°, 65° d. None of the above

#### Solution:

In an isosceles triangle, two angles are equal.

A triangle with angle measures 50°, 50°, 80° and 50°, 65°, 65° forms an isosceles triangle.

Among the choices, a triangle with angle measures 50°, 60°, and 80° cannot form an isosceles triangle.

9.
Which of the figures is an obtuse triangle?  a. Figure 4 b. Figure 3 c. Figure 2 d. Figure 1

#### Solution:

Figures 1 and 3 are acute triangles.
[All the angles are less than 90o.]

Figure 2 is a right triangle.
[One angle is 90o.]

Figure 4 is an obtuse triangle.
[One angle is greater than 90o.]

10.
O is the center of the circle. Are the triangles COB and COD isosceles triangles?  a. No b. Yes

#### Solution:

A triangle with two congruent sides is an isosceles triangle.

CO, DO and BO are the radii of the circle.

In a circle, all radii have equal measures.

ΔCOB is an isosceles triangle.
[Since CO = BO]

Similarly, in ΔCOD, measures of segments CO and OD are equal.

ΔCOD is an isosceles triangle.

So, the triangles COB and COD are isosceles triangles.