The Triangle and Its Properties Test

Result

The Triangle and Its Properties Test - 5

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Question 1
1 / -0

State 'T' for true and 'F' for false.

(i) Triangle can have two angles of 90°.
(ii) In a triangle, if there are two acute angles, then third one would be an obtuse angle.
(iii) In a right angle triangle, there are always two acute angles.

(i) (ii) (iii)

A T T T

B T F T

C F F T

D F F F

A
A

B
B

C
C

D
D

Solution

(i) Triangle cannot have two angles of 90°, so given statement is false. Right triangle has one 90 degree angle and two acute (< 90 degree) angles.

(ii) In a triangle, if there are two acute angles, then third one could be an obtuse angle or it could be an acute angle as well, so given statement is false. An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles.

(iii) In a right angle triangle, there are always two acute angles. So, given statement is true. If a triangle has two acute angles and a single right angle, then the triangle is called a right triangle.
Question 2
1 / -0

In this question, three statements are given with some blanks. Fill in the blanks with the help of the table given below.

(i) A triangle can have maximum A altitudes.
(ii) The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is B .
(iii) If the base of a right-angled triangle is 8 cm and its perpendicular is 15 cm, then the length of hypotenuse will be C cm.

Options (i) (ii) (iii)

A 3 90° 15

B 3 90° 17

C 2 105° 15

D 3 105° 17

A
A

B
B

C
C

D
D

Solution

(i) A triangle can have maximum 3 altitudes.

(ii) Let the angles be x, 2x and 3x.

Now,
x + 2x + 3x = 180° (Angle sum property of triangle)

6x = 180°
x = 30°

Largest angle = 3x = 3 × 30° = 90°

(iii) According to Pythagoras Theorem,

(Hypotenuse)² = (Base)² + (Perpendicular)²

Here,

(Hypotenuse)² = (8)² + (15)²

(Hypotenuse)² = 64 + 225 = 289

Hypotenuse = 17 cm