Differences of segments/angles
If AC = 15 and AB = 9, where A—B—C, find BC.
BC=6
How many equal sides and angles does an equilateral triangle have? What is each interior angle measure?
3 equal sides. 3 equal angles
In a parallelogram, one angle measures 62°. What are the measures of the other three angles?
62°, 62°, 118°, 118°
Define the radius and diameter of a circle and state their relationship
Radius = the distance from the center of the circle to a point on the circle
An inscribed angle intercepts an arc measuring 110 degrees. Find the measure of the inscribed angle.
550
On a line, M is between P and Q. If PQ = 22 and PM = 8, find MQ.
MQ=14
If an equilateral triangle has a side length of 6 cm, find its perimeter and area (exact form).
18 cm; 9sqrt(3) cm2
Two lines intersect so that one angle is (3x + 8)° and an adjacent angle is (2x − 13)°. Find all four angle measures.
x=370; 610, 610, 1190, 1190
An arc of a circle subtends a central angle of 72° in a circle of radius 10. Find the measure of the major arc.
2880
Write the standard equation of a circle centered at
(3, −2) with radius 4.
(x-3)2+(y+2)2=16
AB = 4x + 1, AC = 11x − 5, BC=22, and B is between A and C. Find x, AB, AC.
x=4, AB=17, AC=39
Side lengths of an equilateral triangle are doubled. How does the area change?
4 times greater
Given coordinates A(1,2), B(5,2), C(4,−1), D(0,−1), what type of quadrilateral is ABCD?
parallelogram
If sin θ = 3/5 for acute θ, find cos θ.
4/5
Triangle ABC ~ Triangle DEF. If AB = 8, BC = 10, and DE = 12, find EF.
15
Two angles differ by 40°. If the larger angle is 3 times the smaller, find both angles.
x=200, 3x=600
In an isosceles triangle, the vertex angle is 20° less than each base angle. Find all angles (degrees and minutes; 1 degree=60 minutes).
460 40', 660 40', 660 40'
A right triangle has an acute angle of 30°. What are the exact values of sin(30°) and cos(30°)?
1/2; sqrt3/2
A ladder leans against a wall, making a 65° angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach? (Give the answer to two decimal places.)
10 sin 650 approx 9.06
A quadrilateral is inscribed in a circle. Two of its angles measure 70° and 130°.
1100, 500
Angles X and Y are supplementary and X − Y = 28°. Find X and Y.
x=1040, y=760
Sides of an isosceles triangle are 7, 7, and 10. Find the perimeter and classify by angle (acute/obtuse/right)
72+72 < 102, so an acute triangle
Given △ABC and △A'B'C' are similar. Coordinates: A(0,0), B(4,0), C(0,3). The image △A'B'C' is translated. If A' maps to (2,1) and B' maps to (6,1), find the coordinates of C'.
(2,4)
A chord is 12 cm from the center of a circle with a radius of 13 cm. Find the chord's length.
10 cm
Write the standard equation of the circle with diameter endpoints A(−1, 2) and B(5, 8).
(x-2)2+(y-5)2=72