Construcing a 60° Angle and Properties of 30°-60°-90° Triangles

Complete the construction by drawing segment . Consider the triangle and describe its characteristics, showing why angle measures . (Use the Undo and Redo buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).

Calculate the length of the height relative to side of the triangle below, using the available information.

Describe the properties of triangles with interior angles .

A very creative architect decides to tile a kitchen countertop using triangular tiles. Each tile has one side measuring cm, another side meausring cm, and the angle opposite the cm side is . What is the shape of each tile? Draw it. Tiles are sold in boxes, each containing square meters of tiles . How many boxes must the architect buy to have enough tiles to cover the entire kitchen countertop?

If a statement is false, correct it to make it true, or provide a counterexample.

1. If the hypotenuse of a triangle with angles measures m, also one of the legs of the triangle measures m.
2. If the base of a triangle with angles measures m, the height relative to side splits that side into two segments, each measuring m.
3. Two triangles with corresponding angles measuring are congruent.
4. An equilateral triangle can be always obtained by mirroring a triangle with angles