Construct $△ H A T$ such that $H A = A T = 5 c m$ and $∠ A = 60 °$ . What are the measures of other two angles of the triangles? What type of triangle is this?

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Solution

STEPS OF CONSTRUCTION:
STEP 1: First we draw a line segment $H A$ of length $5 c m$ .
STEP 2: Now we make a ray $A X$ such that $∠ H A X = 60 °$ .
STEP 3: With $A$ as centre and $5 c m$ as radius draw an arc intersecting $A X$ at $T$ .
STEP 4: Now join $H T$ and we get the required triangle $H A T$ .
$∠ H A T + ∠ A H T + ∠ H T A = 180 ° . . . (b y a n g l e s u m p r o p e r t y) 60 ° + x + x = 180 ° (∠ A H T = ∠ H T A = x) 60 ° + 2 x = 180 ° 2 x = 180 ° - 60 ° 2 x = 120 ° x = \frac{120 °}{2} = 60 °$
So the other two angles are also $60 °$ .
This is an equilateral triangle.

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Construct △HAT such that HA=AT=5cm and∠A=60°. What are the measures of other two angles of the triangles? What type of triangle is this?

Construct $△ H A T$ such that $H A = A T = 5 c m$ and $∠ A = 60 °$ . What are the measures of other two angles of the triangles? What type of triangle is this?