Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm. Class 8

Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm. Class 8

Question 1.

Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm. Class 8

Solution:

All sides AB, AC, BD and CD are of length 4 cm.

∠BDC = 60°

and ∠ABD = ∠ACD = 60° + 60° = 120°.

Question 2.

Construct a kite whose diagonals are of lengths 6 cm and 8 cm.

Solution:

Step 1. Draw a line segment AB = 8 cm.

Step 2. Take any point P on AB and construct a perpendicular XPY to AB.

tep 3. With P as centre and [latex]\frac{1}{2}[/latex](6 cm) as radius, draw an arc to intersect line XY at C and D.

Step 4. Join AC, BC, BD and AD.

Then, ACBD is the required kite.