Question

turning into triangles

1. construct a segment. label the endpoints a and b.
2. rotate segment ab clockwise around center b by 90 degrees. label the new endpoint a.
3. use the polygon tool to draw triangle aba.

what kind of triangle did you draw? what other properties do you notice in the figure? explain your reasoning. for example, you could use the circle tool to verify lengths. you could use the angle tool to measure angles.

Explanation:

Step1: Analyze rotation property

When segment AB is rotated 90 - degrees clock - wise around B to get A', then $\angle ABA'=90^{\circ}$.

Step2: Analyze side - length property

Since rotation is a rigid transformation, $AB = BA'$.

Step3: Determine triangle type

A triangle with a 90 - degree angle and two equal sides is an isosceles right - triangle. The two equal sides are AB and BA', and the right - angle is $\angle ABA'$. Also, the non - right angles $\angle BAA'$ and $\angle BA'A$ are equal. Using the angle - sum property of a triangle ($\angle BAA'+\angle BA'A+\angle ABA' = 180^{\circ}$), and since $\angle ABA'=90^{\circ}$, then $\angle BAA'=\angle BA'A = 45^{\circ}$.

Answer:

The triangle drawn is an isosceles right - triangle. The properties are: it has a right angle ($\angle ABA' = 90^{\circ}$), two equal sides ($AB = BA'$), and the non - right angles are both 45 degrees ($\angle BAA'=\angle BA'A = 45^{\circ}$).