# Triangles and Quadrilaterals Exploration

From EscherMath

**Objective:**

Triangles can be combined to create other shapes. This fact will be used later in the course.

### Equipment

Start this activity with four congruent 30°-60°-90° triangles.

### Questions

- Measure, in centimeters, the three sides of your triangle. Try to find some relationship between your angle measures and the measures of the sides.
- Put two triangles together with no gaps and no overlapping to obtain an equilateral triangle. How many lines of symmetry does an equilateral triangle have?
- Put two of the triangles together to obtain an isosceles triangle. (That is not also equilateral.)
- What does the
*line down the middle*do to the angle of the big triangle? - What does it do to the side it intersects?
- How many lines of symmetry does an isosceles triangle have if it's not equilateral?

- What does the
- Use two of the triangles to form a quadrilateral that is not a parallelogram.
- Use two of the triangles to form a parallelogram that is not a rectangle and not a rhombus. Write down all the things you observe about this new figure. (i.e. angles, lengths of sides, diagonals, symmetry etc.)
- Use two of the triangles to form a rectangle. Record your observations.
- Use four of the triangles to form a rhombus. Record your observations.
- Use all four of the triangles to form another triangle. How does its size and shape compare with the size and shape of the original triangle? What other observations can you make about the new figure?
- Use all four of the triangles to form a square with a square hole in it. This can be done in two ways; sketch them both.
- Which of the questions 2-9 could you do with four congruent triangles that are right triangles, but do not have a 30˚ angle? Try and see.
- Which of the questions 2-9 could you do with four congruent triangles that are not right triangles? Try and see.

**Handin:**
A sheet with answers to all questions.