Lesson 1Relationships of Angles
Learning Goal
Let’s examine some special angles.
Learning Targets
I can find unknown angle measures by reasoning about adjacent angles with known measures.
I can recognize when an angle measures
, , or .
Lesson Terms
- adjacent angles
- right angle
- straight angle
Warm Up: Visualizing Angles
Problem 1
Which angle is bigger,
or ? Identify an obtuse angle in the diagram.
Print Version
Which angle is bigger?
Identify an obtuse angle in the diagram.
Activity 1: Pattern Block Angles
Problem 1
Look at the different pattern blocks inside the applet. Each block contains either 1 or 2 angles with different degree measures. Which blocks have only 1 unique angle? Which have 2?
If you place three copies of the hexagon together so that one vertex from each hexagon touches the same point, as shown, they fit together without any gaps or overlaps. Use this to figure out the degree measure of the angle inside the hexagon pattern block.
Figure out the degree measure of all of the other angles inside the pattern blocks. (Hint: turn on the grid to help align the pieces.)
Print Version
Trace one copy of every different pattern block. Each block contains either 1 or 2 angles with different degree measures. Which blocks have only 1 unique angle? Which have 2?
If you trace three copies of the hexagon so that one vertex from each hexagon touches the same point, as shown, they fit together without any gaps or overlaps. Use this to figure out the degree measure of the angle inside the hexagon pattern block.
Figure out the degree measure of all of the other angles inside the pattern blocks that you traced in the first question. Be prepared to explain your reasoning.
Are you ready for more?
Problem 1
We saw that it is possible to fit three copies of a regular hexagon snugly around a point.
Each interior angle of a regular pentagon measures
Activity 2: More Pattern Block Angles
Problem 1
Use pattern blocks to determine the measure of each of these angles.
Print Version
Use pattern blocks to determine the measure of each of these angles.
Problem 2
If an angle has a measure of
Use the applet if you choose. (Hint: turn on the grid to help align the pieces.)
Print Version
If an angle has a measure of
Activity 3: Measuring Like This or That
Problem 1
Tyler and Priya were both measuring angle
Priya thinks the angle measures 40 degrees. Tyler thinks the angle measures 140 degrees. Do you agree with either of them? Explain your reasoning.
Lesson Summary
When two lines intersect and form four equal angles, we call each one a right angle. A right angle measures
An angle in which the two sides form a straight line is called a straight angle. A straight angle measures
If you put two straight angles together, you get an angle that is
When two angles share a side and a vertex, and they don’t overlap, we call them adjacent angles.