# Relationships of Angles

Warmup

Use the applet to answer the questions.

(1.) Which angle is bigger, a or b ?

(2.) Identify an obtuse angle in the diagram.

Activity #1

Relationship of Angles. • Drag A, B, C or D so that AB is parallel to CD. As soon as they are parallel, you’ll see 2 marked angles in red.​
• Check 2nd pair, 3rd pair, and 4th pair to see corresponding angles.
• Now, check Alternate angles, and check 2nd pair to see another pair of alternate angles.
• Check Interior angles on the same side to see the co-interior angles.
• Click the reset button and click on “Horizontal” repeat the steps above.
• Click the reset button and click on “Vertical”, and also repeat the steps above.

(1.) What do you notice observe about corresponding angles? You can check “Theorem” to answer this question.

(2.) How many pairs of corresponding angles are formed when a transversal crosses two parallel lines?

(3.) How many pairs of alternate angles are formed when a transversal crosses two parallel lines?

(4.) How many pairs of co-interior angles are formed when a transversal crosses a pair of parallel lines?

Activity #2

Look at the different pattern blocks inside the applet below. Each block contains either 1 or 2 angles with different degree measures. • Interact with applet below and answer the questions that follow.

(1.) Which blocks have only 1 unique angle?

(2.) Which blocks have 2 unique angles?

(3.) If you place three copies of the hexagon together so that one vertex from each hexagon touches the same point, they fit together without any gaps or overlaps. Use this to figure out the degree measure of the angle inside the hexagon pattern block. (4.) Figure out the degree measure of all of the other angles inside the pattern blocks.

(5.) We saw from above that it is possible to fit three copies of a regular hexagon snugly around a point. Each interior angle of a regular pentagon measures 108°. Now, many copies does it take to fit three copies of a regular hexagon snugly around a point?

Activity #3

Explore Angles in a Polygon. • Use the blocks to help you find the angles in the applet below. (Hint: turn on the grid to help align the pieces. Remember to click on the block to rotate it.)

(1.) What is the value of angle a ?

(2.) What is the value of angle b ?

(3.) What is the value of angle c ?

Challenge #1

Click on an angle type in the app below and name another pair of the same type.

(1.) Another pair of alternate exterior angles.

(2.) Another pair of alternate interior angles.

(3.) Another pair of corresponding angles.

(4.) Another pair of same side interior angles.

(5.) Another pair of same side exterior angles.

Challenge #2

Use the applet below to draw a right angle.

(1.) How do you know it’s a right angle?

(2.) What is its measure in degrees?

Quiz Time