options: Understand and apply the Pythagorean Theorem.

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

Use coordinates to prove simple geometric theorems algebraically.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

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

Understand congruence in terms of rigid motions.

Make geometric constructions.

Experiment with transformations in the plane.

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

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

Prove theorems involving similarity.

Understand and apply theorems about circles.

Apply trigonometry to general triangles.

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

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

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

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

Prove geometric theorems.

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

Explain volume formulas and use them to solve problems.

Reason with shapes and their attributes.

Understand similarity in terms of similarity transformations.

Define trigonometric ratios and solve problems involving right triangles.

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

Analyze, compare, create, and compose shapes.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
problem_activity: Problem 1
Your group should have a few copies of
Handout #2
and a set of cards from
Handout #1
.
Draw three cards and place them in the appropriate places on the Handout #2 form. This represents three conditions about a triangle. Once you’ve placed them on the form, do not change the order.
Determine if the set of conditions will make one unique triangle, more than one triangle, or no triangle.
If you can make one unique triangle, draw and label the triangle.
If more than one or no triangle can be made, be prepared to explain your reasoning.
Choose another three cards and repeat the activity.
Problem 2
Two triangles are described below. Determine if each description results in one unique triangle, more than one triangle, or no triangle. Explain your reasoning or draw images to support your conclusion.
a.   Triangle
$${EFG}$$
is an isosceles triangle with two angles measuring 35°. Side length
$${EG}$$
measures 10 cm.
b.   Triangle
$${{PQ}R}$$
is an isosceles triangle with
$${\angle P}$$
and
$${\angle Q}$$
measuring 22°. Side length
$${PQ}$$
measures 8 cm.


correct_option_index: 9