what type is triangle is triangle abc? give your reasons
Answers
Answer:
Because in an isosceles ∆ two angles are equal
Step-by-step explanation:
Angle C= 80°
Angle ACD+Ang.ACB+AngBCE=180°
50°+ACB+80°=180°
130°+ACB=180°
ACB=180°-130°
ACB=50°
Now In ∆ABC
ang.A+ang.B+ang.C=180°
A+ 80°+50°=180°
A+130°=180°
A=180°-130°
A=50°
Now angle A=C=50°
Hence proved that ∆ABC is an isosceles triangle
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°
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