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

Find arc lengths and areas of sectors of circles.

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

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

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

Make geometric constructions.

Reason with shapes and their attributes.

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

Experiment with transformations in the plane.

Explain volume formulas and use them to solve problems.

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

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

Apply trigonometry to general triangles.

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

Understand similarity in terms of similarity transformations.

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

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

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

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

Understand and apply theorems about circles.

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

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

Prove geometric theorems.
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: 24