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

Apply trigonometry to general triangles.

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

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

Prove geometric theorems.

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

Make geometric constructions.

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

Prove theorems involving similarity.

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

Analyze, compare, create, and compose shapes.

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

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

Experiment with transformations in the plane.

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

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Problem 1
Pentagon
$${FGHIJ}$$
is a scale image of pentagon
$${ABCDE}$$
.
[IMG]
a.   Complete the table below with the measurements of each pentagon.
| **                Original line segment               ** | **                Original length               ** | **                Corresponding line segment               ** | **                Scale length               ** |
|----------------------------------------------------------|----------------------------------------------------|---------------------------------------------------------------|-------------------------------------------------|
|                          $$AB$$                          |                                                    |                            $$FG$$                             |                                                 |
|                          $$BC$$                          |                                                    |                            $$GH$$                             |                                                 |
|                          $$CD$$                          |                                                    |                            $$HI$$                             |                                                 |
|                          $$AE$$                          |                                                    |                            $$FJ$$                             |                                                 |
b.   Is there a proportional relationship between the side lengths of the original pentagon and the scaled pentagon? Explain using the measurements in the table.
c.   What is the constant of proportionality?
d.   What is the scale factor?
Problem 2
Melissa orders business cards to promote her new website. She previews the cards online before placing her order. The scale image she sees online and the actual size of the cards are shown below.
[IMG]
What scale factor was used to create the online image from the actual size of the business card?
Problem 3
For each situation described below, sketch and label the scale image using the scale factor.
a.   Your family recently had a family portrait taken. Your aunt asks you to take a picture of the portrait using your phone and send it to her. The original portrait is 3 feet by 3 feet and the scale factor from the original picture to the picture on your phone is
$${1 \over18}$$
. Draw the scale drawing, in inches, that would be the size of the portrait on your phone.
b.   Create a scale drawing of the arrow below using a scale factor of 150%.
[IMG]


correct_option_index: 0