Practice Set 2
10 Connected Questions
This set focuses on radians and sectors, similarity, right triangle trigonometry, coordinate geometry, and measurement models.
Practice Questions
DOK 2 Practice Set: Geometry Connections
Use Desmos to compare circle measures, coordinate points, and triangle relationships while you connect formulas to geometry meaning.
Question 1
A circle has radius 6 and central angle π/2 radians. What is the arc length?
Desmos Move: Use s = rθ when the angle is already measured in radians.
Question 2
What is the area of a 120° sector in a circle with radius 9?
Desmos Move: A 120° sector is one third of the full circle, so take one third of πr².
Question 3
Two similar triangles have a scale factor of 10/4 from small to large. If a side on the small triangle is 6, what is the matching side on the large triangle?
Match corresponding sides, then apply the same scale factor.
Desmos Move: Multiply the known side by the scale factor instead of setting up separate addition.
Question 4
A ramp rises 3 feet over a horizontal run of 12 feet. Which angle measure is closest to the angle of elevation?
Desmos Move: Use tan⁻¹(opposite/adjacent) with opposite 3 and adjacent 12.
Question 5
The endpoints of a diameter are (-6, 4) and (2, -2). What is the center of the circle?
Desmos Move: The center of a diameter is the midpoint of its endpoints.
Question 6
Find the distance between (-2, 1) and (4, 9).
Desmos Move: The changes are 6 and 8, so this becomes a 6-8-10 right triangle.
Question 7
If the scale factor between two similar figures is 3, what is the area scale factor?
Desmos Move: Area changes by the square of the linear scale factor.
Question 8
Which statement is true about a triangle with side lengths 9, 12, and 15?
Desmos Move: Check whether the longest side squared equals the sum of the other two squares.
Question 9
A cylinder has diameter 10 and height 12. What is its volume to the nearest whole number?
Desmos Move: Convert diameter to radius first, then use V = πr²h.
Question 10
A sector has arc length 5π and radius 10. What is its central angle in radians?
Desmos Move: Use θ = s/r when the arc length and radius are known.