Table of Contents

- 1 What triangles make a parallelogram?
- 2 What is the relationship between a parallelogram and a triangle?
- 3 Can a triangle be a parallelogram?
- 4 Can a parallelogram be divided into two triangles?
- 5 Is a parallelogram a triangle?
- 6 How are parallelograms related to triangles and rectangles?
- 7 Can the same pair of triangles make a parallelogram?
- 8 How many parallel sides does a trapezoid have?

## What triangles make a parallelogram?

A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices. Going the other way around, two identical copies of a triangle can always be arranged to form a parallelogram, regardless of the type of triangle being used.

## What is the relationship between a parallelogram and a triangle?

If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram. If they have same altitude, they will lie between the same parallels. Hence the area of the triangle will be equal to half that of the parallelogram.

**How is area of parallelogram and triangle related?**

Area of a triangle is ½ x base x height. If a triangle and parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of a parallelogram.

**Can a parallelogram be formed by congruent triangles?**

Diagonals in Parallelograms A diagonal acts as a transversal and creates alternate interior angles with the parallel sides. When both diagonals are drawn, two pairs of congruent vertical angles are formed. When one diagonal is drawn in a parallelogram, two congruent triangles are formed.

### Can a triangle be a parallelogram?

A triangle is a parallelogram. This is never true. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

### Can a parallelogram be divided into two triangles?

Solid Facts. A parallelogram is a quadrilateral that has both pairs of opposite sides parallel. Theorem 15.5: A diagonal of a parallelogram separates it into two congruent triangles.

**Can a parallelogram be a triangle?**

**Are a parallelogram and a triangle similar?**

If ABCD is a parallelogram and P, Q (positioned as shown in the applet) are such that triangles PAB and BCQ are similar (with P corresponding to B, A to C, and B to Q), then each is similar to triangle PDQ. …

## Is a parallelogram a triangle?

A triangle is a parallelogram. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Since a parallelogram’s opposite sides are congruent and parallel, one can translate the right triangle to the opposite side of the parallelogram and recompose it, as shown in the second figure on the right. The result is a rectangle with the same length base and height as the original parallelogram.

**Is a triangle a parallelogram?**

**What divides a parallelogram into two congruent triangles?**

Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles. Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. You can show that alternate interior angles are congruent and hence lines are parallel for this part of the proof.

### Can the same pair of triangles make a parallelogram?

To produce a parallelogram, we can join a triangle and its copy along any of the three sides, so the same pair of triangles can make different parallelograms. Here are examples of how two copies of both Triangle A and Triangle F can be composed into three different parallelograms.

### How many parallel sides does a trapezoid have?

Guide students to recall that a trapezoid as a quadrilateral with exactly one pair of parallel sides. Have students cut along the crease. Label the new triangle 7(Figure 3). 9. Have students again write statements using “subdivide” and “combine” to describe the relationship between the large triangle, small triangle, and trapezoid.

**How many small triangles can be combined to form one large triangle?**

A large triangle can be subdivided into two smaller triangles. Two small triangles can be combined to form one large triangle. 7. Ask the following questions to discuss these two new polygons: “Who can describe these new polygons?

**What is the base of the parallelogram on the left?**

The base of the parallelogram on the left is 2.4 centimeters; its corresponding height is 1 centimeter. Find its area in square centimeters. The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? Explain your reasoning.