Sums of Angles in Triangles and Quadrilaterals

Melissa McGarity

Objectives: Students will explore the sums of angles of triangles and quadrilaterals. Students will be able to find the measurement of an unknown angle of a triangle or a quadrilateral.

Materials: GSP file and worksheet

Sums of Angles in Triangles and Quadrilaterals

NAME:_________________________

Instructions: Open and use the GSP file "trianglesums" for questions 1 - 4.

1. For Triangle XYZ, find the measurement for each of its angles.

X = _____

Y = _____

Z = _____

Classify this triangle by its angle measurements. __________________

What do you get if you find the sum of the three angles of this triangle? _________

2. For Triangle TUV, find the measurement for each of its angles.

T = _____

U = _____

V = _____

Classify this triangle by its angle measurements. __________________

What do you get if you find the sum of the three angles of this triangle? _________

3. For Triangle QRS, find the measurement for each of its angles.

Q = _____

R = _____

S = _____

Classify this triangle by its angle measurements. __________________

What do you suspect about the sum of the angles in this triangle?

What do you get if you find the sum of the three angles of this triangle? _________

4. Now look at Triangle LMN. What conjecture do you have about the sum of the angles? Write a complete sentence!

Verify your conjecture using the measurements of the angles.

Instructions: Open the GSP file "quadsums" to answer questions 5 - 8.

5. For Quadrilateral ABCD, find the measurements for each of its angles.

A = _____

B = _____

C = _____

D = _____

Find the sum of the four angles of this quadrilateral. What is it?__________

6. For Quadrilateral EFGH, find the measurements of each of its angles.

E = _____

F = _____

G = _____

H = _____

What is the sum of the four angles?_________

7. What do you suspect about the sum of the angles of Quadrilateral IJKL?

Find the measurements of the angles to help verify your suspicions.

8. Show that the sum of the angles of Quadrilateral MNOP is 360` degrees.`

```9. How would you find the measurement of an unknown angle in a triangle if the other two angle measurements are known?```

```10. How would you find the measurement of an unknown angle in a quadrilateral if the other three angle measurements are known?```

`Instructions: ````Find the measurement of each unknown angle. Assume all angle measurements are in degrees.```