Question

What type of triangle is abc? give reasons for your answer. i know it's isosceles but i don't know the reasons... so i'm asking for help. thanks!

Answer 1

Given : ΔABC , AD || DE , C lies on DE

∠ABC = 80° , ∠ACD = 50°

To Find : Type of triangle

Solution :

Properties of angles formed by transversal line with two parallel lines :

• Corresponding angles are congruent. ( Equal in Measure)

• Alternate angles are congruent. ( Interiors & Exterior both )

• Co-Interior angles are supplementary. ( adds up to 180°)

Sum of angled of a triangle = 180°

AD || DE and AC is transversal

∠CAB = ∠ACD Interior alternate angles

=> ∠CAB = 50°

Sum of angled of a triangle = 180°

=> ∠CAB + ∠ABC + ∠BCA = 180°

=> 50° + 80° + ∠BCA = 180°

=> ∠BCA =50°

∠CAB = ∠BCA =50°

Two angles are equal

Hence Triangle is Isosceles triangle

All 3 angles are acute angles

Hence triangle is Acute triangle

Additional Info :

Types of triangles

Equilateral : All sides are equal

Isosceles : two sides are equal

Scalene : All 3 sides are of different length

Right angle triangle - One angle is Right angle

Obtuse Triangle - one angle is greater than 90°

Acute Triangle - All three angles are less than 90°