Equilateral and Isosceles Triangle

An equilateral triangle in which all three sides have the same length.

All sides of an equilateral traingle are equal.

$$
$ABC$ is an equilateral triangle. Find the measures of the angles marked $x, y$ and $z$. 

Construct an isosceles triangle PQR in which side PQ = PR $= 5$ cm and height PS $= 2.5$cm. 

D is a point on the side BC of an equilateral triangle ABC such that $BD : DC = 2 : 1.$ Prove that $9A{D}^2= 7 A{B}^2.$

The triangle is called isosceles when its _____ sides are equal. 

If all three side of a triangle are equal, then all the angles will be acute angle. Write "Yes" or "No" as final answer.

The perpendicular drawn from the vertex to the opposite side bisects the base of isosceles and _____triangles.