Geometric Gems Assessment Worksheet
Geometry Mastery
30-Question Assessment: Triangles & Circles
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Date:
Part 1
Triangle Tactics (Trig & Pythagorean)
2√2 x 45°
Find hypotenuse x for the 45°-45°-90° triangle if a leg is 2√2.
A) 2
B) 4
C) 4√2
D) 8
16 60° y
In a 30°-60°-90° triangle, find the side opposite 60° (y) if hypotenuse is 16.
A) 8
B) 8√2
C) 8√3
D) 16√3
In ∆ABC, find tan A if the side opposite ∠A is 7 and the side adjacent is 24.
A) 0.28
B) 0.29
C) 3.43
D) 3.57
Find sin A for a right triangle with hypotenuse 17 and side opposite ∠A = 8.
A) 8/15
B) 8/17
C) 15/17
D) 17/8
Calculate hypotenuse x if the side adjacent to a 72° angle is 4.
A) 1.2
B) 4.2
C) 12.3
D) 12.9
A 4.2m ramp (hypotenuse) rises 0.7m. Find the angle of elevation.
A) 9.5°
B) 9.6°
C) 80.4°
D) 80.5°
A 40ft kite string is at 36°. Find the vertical height of the kite.
A) 23.5 ft
B) 29.1 ft
C) 32.4 ft
D) 55.1 ft
3ft 22ft
A 22ft ladder's bottom is 3ft from a wall. Find the angle with the ground.
A) 7.8°
B) 82.2°
C) 83.1°
D) 86.2°
36 64 h
Find altitude h if it divides the hypotenuse into segments of 36 and 64.
A) 48
B) 50
C) 60
D) 100
Which set of side lengths represents a Pythagorean triple?
A) 2, 4, 8
B) 5, 6, 7
C) 6, 8, 15
D) 9, 12, 15
Plane rises 325m vertically then flies east 500m. Find displacement.
A) 596m
B) 600m
C) 825m
D) 1625m
Find the geometric mean of the numbers 4 and 18.
A) 6√2
B) 11
C) 36
D) 72
Side lengths 5, 6, and 7 form which type of triangle?
A) Acute
B) Obtuse
C) Right
D) Not tri.
In a 30°-60°-90° triangle, if hypotenuse is 10, find shorter leg.
A) 5
B) 5√3
C) 10
D) 20
Find the value of cos 66° rounded to the nearest hundredth.
A) 0.41
B) 0.44
C) 0.91
D) 2.25
Part 2
Circle Secrets
A line that intersects a circle at exactly two points is a:
A) Radius
B) Secant
C) Tangent
D) Chord
Which segment has endpoints that both lie on the circle?
A) Chord
B) Diameter
C) Both A/B
D) Secant
A tangent line is ________ to the radius at the pt. of tangency.
A) Parallel
B) Perp.
C) Skew
D) Supp.
Ext. Pt
Tangent segments from an external point have lengths 7x - 13 and 9x - 23. Find x.
A) 5
B) 10
C) 18
D) 22
x 24 16 ext.
Radius is x. Tangent segment is 24, ext. distance is 16. Find x.
A) 8
B) 10
C) 12
D) 14
An arc that measures exactly half the circle (180°) is a:
A) Minor
B) Major
C) Semicircle
D) Sector
63°
Central angle is 63°. Find measure of intercepted minor arc.
A) 31.5°
B) 63°
C) 126°
D) 297°
Minor arc is 47°. Measure of the corresponding major arc?
A) 133°
B) 227°
C) 313°
D) 360°
63°
Vertical central angles: if one arc is 63°, the other vertical arc is:
A) 27°
B) 63°
C) 117°
D) 180°
True or False: Arcs are congruent if they have same measure & same/congruent circle.
A) True
B) False
140° 80°
Find measure of arc BCD if m(arc BC) = 140° and m(arc CD) = 80°.
A) 60°
B) 140°
C) 220°
D) 360°
The point where a tangent line contacts a circle is the:
A) Center
B) Pt of tangency
C) Vertex
D) Focus
Congruent circles must have radii of the same length.
A) True
B) False
Notation for a major arc typically requires how many points?
A) 1
B) 2
C) 3
D) 4
240°
Major arc is 240°. Find central angle of the minor arc.
A) 60°
B) 120°
C) 180°
D) 240°
Scratchpad / Calculations
