DOK 3 Practice Set: Geometry Reasoning

Use Desmos when helpful to test right triangle values, scale relationships, and measurement reasonableness while you work through richer geometry tasks.

Practice Set 3

10 Strategic Questions

This set focuses on similarity justification, trig modeling, radian reasoning, scale drawings, coordinate geometry, and volume or surface-area interpretation.

10 questionsDOK 3 review

Question 1

Triangles A and B have side lengths 6, 8, 10 and 9, 12, 15. Which statement best justifies that the triangles are similar?

DOK 3

Desmos Move: Check whether each side in one triangle is multiplied by the same scale factor.

Question 2

A 20-foot ladder makes a 53° angle with the ground. About how high up the wall does it reach, to the nearest foot?

DOK 3

Use the given angle and hypotenuse to find the height on the wall.

Numeric response

Desmos Move: Use sin(53°) = height / 20 because the height is opposite the angle.

Question 3

A sector has arc length 12 and radius 8. Which value is the best estimate of its central angle in radians?

DOK 3

Desmos Move: Use θ = s/r when you know arc length and radius.

Question 4

On a scale drawing, 1 inch represents 4 feet. A triangular patio measures 3 inches, 4 inches, and 5 inches on the drawing. What is the actual perimeter?

DOK 3

Desmos Move: Convert each side using the scale factor, then add the actual lengths.

Question 5

A cylindrical can has radius 4 and height 12. If you only cover the curved side, what is the lateral surface area to the nearest whole number?

DOK 3

Numeric response

Desmos Move: For lateral surface area of a cylinder, use 2πrh and do not add the top and bottom.

Question 6

Which statement is always true about similar figures?

DOK 3

Desmos Move: Similarity keeps shape the same while allowing a scale change in size.

Question 7

A 6-foot person casts a 4-foot shadow at the same time a tree casts an 18-foot shadow. About how tall is the tree?

DOK 3

Desmos Move: Set up a proportion using matching height-to-shadow ratios from similar triangles.

Question 8

What is the midpoint of the segment joining (-5, 7) and (9, -1)?

DOK 3

Desmos Move: Average the x-values and y-values separately.

Question 9

If a solid is enlarged by a linear scale factor of 2, what is the volume scale factor?

DOK 3

Desmos Move: Volume changes by the cube of the linear scale factor.

Question 10

Which formula gives the area of a sector when θ is measured in radians?

DOK 3

Desmos Move: Do not switch back to degrees. Use the radian version of the sector area formula directly.