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°