Construct the following traingles

Question

Q. Construct a triangle ABC in which Q1. Angle A=120°, angle B=30° and angle C=30°. Q2. Angle A=90°, angle B=60° and angle C=30°. Q3. Angle A= angle B= angle C= 60°.

Answer 1

The diagram illustrates the construction of the figures for all three questions.

The colours aid in the descriptions below. Mark C as the intersection of the two circles.

Q1.

Draw a (red dotted) circle centre A and draw an extended diameter where black B to green B is the diameter.

With centre at green B draw a second (red dotted) circle of the same size. Join C to black B and A. This is the required triangle. Draw the same size circle with centre green B.

Q2.

With centre at black B and radius beyond A draw a (blue dotted) circle. With centre at green B draw another (blue dotted) circle which intersects the other circle. Draw a line from the intersection cutting through red BC at blue C. This gives us the right triangle formed by A, B and blue C.

Q3.

Join red C to A and green B. The green triangle is the required one.