Triangles - Study Mode

[#1] If angle bisector of a triangle bisects the opposite side, then what type of triangle is it?
Correct Answer

(C) Isosceles and equilateral

Explanation

Solution: According to question, AB = AC BD = DC The triangle will be isosceles and equilateral triangle

[#2] If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is
Correct Answer

(A) 3 units

Explanation

Solution: According to question, ABC is a right angle triangle By using Pythagoras theorem AC 2 = BC 2 + AB 2 5 2 = 3 2 + 4 2 25 = 9 + 16 25 = 25 (satisfied) ∴ Smallest length of right angle triangle is 3 units

[#3] In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is:
Correct Answer

(D) 29°

Explanation

Solution: According to question, Given : AC = CD ∠BAD = 111° ∠ACB = 80° ∴ ∠ACD = 180° - 80° ∠ACD = 100° In isosceles triangle ACD ∠ACD + ∠CAD + ∠ADC = 180° 2∠CAD = 180° - 100° ∠CAD = 40° ∴ ∠CAB = 111° - 40° = 71° ∴ ∠ABC = 180° - 71° - 80° ∠ABC = 29°

[#4] In a ΔABC, AB = BC, ∠B = x° and ∠A = (2x - 20)°, Then ∠B is :
Correct Answer

(D) 44°

Explanation

Solution: According to question, Given : AB = AC ∠C = ∠A = 2x - 20° ∠B = x° As we know that ∠A + ∠B + ∠C = 180° (2x - 20)° + x + (2x - 20)° = 180° 5x = 220° x = 44° ∴ ∠B = 44°

[#5] If two angles of a triangle are 21° and 38°, then the triangle is :
Correct Answer

(C) Obtuse-angled triangle

Explanation

Solution: According to question, Given : ∠A = 21°, xa0 xa0 xa0 ∠C = 38° As we know that ∠A + ∠B + ∠C ∠B = 180° - 21° - 38° ∠B = 121° ∴ The triangle is obtuse-angled triangle.