options: Analyze, compare, create, and compose shapes.

Define trigonometric ratios and solve problems involving right triangles.

Classify two-dimensional figures into categories based on their properties.

Prove theorems involving similarity.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand congruence in terms of rigid motions.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Translate between the geometric description and the equation for a conic section.

Understand similarity in terms of similarity transformations.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

Solve real-world and mathematical problems involving area, surface area, and volume.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Find arc lengths and areas of sectors of circles.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Prove geometric theorems.

Visualize relationships between two-dimensional and three-dimensional objects.

Make geometric constructions.

Apply trigonometry to general triangles.

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.
problem_activity: Warm-up
In this activity, students practice determining the measurement of unknown angles using their relationship to angles with known angle measure and what students already know about the measurement of right angles and straight angles. After they have worked on the activity and shared their solutions, they are introduced to the vocabulary terms complementary and supplementary. Complementary describes angles whose measures sum to 90 degrees and supplementary describes angles whose measures sum to 180 degrees.
Some students may wish to use protractors, either to double check work or to investigate the different angle measures. This is an appropriate use of technology (MP5), but ask these students what other methods they could use instead.
Launch
Provide access to geometry toolkits.
Student Facing
Find the measure of angle
\(JGH\)
. Explain or show your reasoning.
[IMG]
Find and label a second
\(30^\circ\)
angle in the diagram. Find and label an angle congruent to angle
\(JGH\)
.
Angle
\(BAC\)
is a right angle. Find the measure of angle
\(CAD\)
.
[IMG]
​​​​​
Student Response
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Anticipated Misconceptions
If needed, remind students that right angles have a measure of
\(90^\circ\)
and straight angles have a measure of
\(180^\circ\)
.
Activity Synthesis
The goal of this discussion is to introduce students to the terms complementary and supplementary for describing relationships between pairs of angles. Display the images for all to see and select students to briefly share their response to each question, recording any calculations used.
Explain to students that the term
complementary
describes a pair of angles whose measures sum to 90 degrees, and the term
supplementary
describes a pair of angles whose measures sum to 180 degrees. This is true even for pairs of angles that are not adjacent. Conclude the discussion by inviting students to identify pairs of angles that are complementary (
\(CAD\)
and
\(DAB\)
), supplementary (
\(FGJ\)
and
\(JGH\)
,
\(JGH\)
and
\(HGI\)
,
\(HGI\)
and
\(IGF\)
, or
\(IGF\)
and
\(FGJ\)
), or vertical (
\(FGJ\)
and
\(HGI\)
or
\(JGH\)
and
\(IGF\)
) from the activity.


correct_option_index: 11