Triangles and Congruence
Triangle ABC has side lengths 7, 24, and 25. What type of triangle is it based on its side lengths?
A scalene triangle
What type of transformation slides a figure without turning it?
Translation
What do you call a segment with both endpoints on the circle?
A chord
What is the slope of a line that passes through the points (–2, 3) and (4, 1)?
-1/3
Find the volume of a rectangular prism with length 5 units, width 3 units, and height 4 units.
60 units3
In triangle ABC, the exterior angle at vertex C measures 120° and ∠A measures 50°. What is the measure of ∠B?
70°
A triangle is reflected across the x-axis. If one vertex was at (3, 4), where is the image of that vertex?
(3, –4)
In a circle, a central angle measures 80°. What is the measure of the intercepted arc?
80°
What is the midpoint of the segment joining (–6, 4) and (2, –2)?
(-2, 1)
A cone has a radius of 3 cm and a height of 9 cm. What is its volume in terms of pi?
27pi cm3
In △ABC and △DEF, AB ≅ DE, ∠B ≅ ∠E, and BC ≅ EF. Which triangle congruence theorem proves △ABC ≅ △DEF?
SAS
What single transformation maps point A(–2, 3) to A′(2, -3)?
180° rotation around the origin
What is the center and radius of the circle with equation (x+3)2+(y–2)2=49
Center (–3, 2) and radius 7
What is the distance between the points A(–3, 7) and B(2, –5)?
13
A block of metal has a volume of 120 cm³ and a mass of 960 g. What is its density?
8 g/cm3
In triangle XYZ, XY ≅ XZ. If ∠Y = 40°, what is the measure of ∠Z?
40°
Which 3 transformation(s) will always preserve both angle measure and side length?
translations, reflections, and rotations
In circle O, arc AC measures 6x–8 degrees. ∠ABC is an inscribed angle that intercepts arc AC and measures 2x+1 degrees. What is the value of ∠ABC?
11°
Given the points A(1, 2), B(4, 6), and C(0, 9), prove that triangle ABC is a right triangle.
AB Slope = 4/3
BC Slope = -3/4
A town has an area of 25 square kilometers and a population density of 150 people per square km. What is the population of the town?
3,750 people
In triangle ABC, D and E are midpoints of AB and AC, and DE is drawn. What is the relationship between DE and BC?
DE is parallel to BC
or
DE = ½ BC
Triangle XYZ has vertices X(–1, 2), Y(3, 2), and Z(0, –1). After a transformation, the image X′Y′Z′ has vertices X′(2, 1), Y′(2, –3), and Z′(-1, 0).
What transformation maps triangle XYZ onto triangle X′Y′Z′?
90° clockwise about the origin
In circle O, chords AB and CD intersect at point E inside the circle. The measure of arc AD is 140°, and the measure of arc BC is 80°. What is the measure of ∠AEC?
70°
Given the vertices of quadrilateral ABCD as A(1, 2), B(5, 5), C(8, 1), and D(4, –2), what is the most specific type of quadrilateral can ABCD be called?
A rectangle
A solid is made of a cylinder with a hemisphere on top. The cylinder has a radius of 3 in and height of 10 in. What is the total volume of the solid to the nearest cubic inch?
339 in3