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

Reason with shapes and their attributes.

Experiment with transformations in the plane.

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

Apply geometric concepts in modeling situations.

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

Explain volume formulas and use them to solve problems.

Make geometric constructions.

Prove geometric theorems.

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

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

Use coordinates to prove simple geometric theorems algebraically.

Find arc lengths and areas of sectors of circles.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

Understand congruence in terms of rigid motions.

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

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

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

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
problem_activity: Problem 1
Brandon and Madison use different triangles to determine the slope of the line shown below.
[IMG]
Brandon started at (0,-1) and drew a right triangle going up 2 units and right 3 units.
Madison started at (-3,-3) and drew a right triangle going up 6 units and right 9 units.
Draw and label both triangles on the graph.
How can Brandon and Madison use their triangles to find the slope?
What trigonometric ratio do Brandon and Madison use to find the slope?
Problem 2
Below is a line segment on a coordinate grid.
[IMG]
Draw the right triangle that you can use to find the length of this line segment.
Find the length of the line segment.
Find the measure of all of the angles of the triangle formed.
Problem 3
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an angle of depression of 20°. The lighthouse is 28 meters tall and sits on a cliff 45 meters tall as measured from sea level.  What is the horizontal distance between the lighthouse and the ship?


correct_option_index: 17