Similarity
Two shapes are considered similar if:
They have the same angles and proportionate sides
If the linear dimensions of a 2D shape are scaled by a factor of k = 3, by what factor does its perimeter increase?
3
In a triangle ABC, line DE is parallel to side BC (with D on AB and E on AC). If AD = 4, DB = 2, and AE = 6, what is the length of EC?
EC = 3
Name a number that does not belong in the set of Natural numbers N
Any negative number
Any partial number
Evaluate the expression: (-8) + (+15) - (+9)
-2
Triangle ABC has side lengths a = 5cm, b = 7cm, and c = 8cm. Triangle DEF is similar to triangle ABC. If the shortest side of triangle DEF is 15 cm, what is the length of its longest side?
24cm
If the scale factor between two similar 2D figures is k = 4, by what factor does its area increase?
16
In Triangle ABC, point D lies on AB and point E lies on AC such that DE is parallel to BC. If AD = 6 cm, AB = 15 cm, and DE = 8 cm, what is the length of BC?
20cm
What is the prime factorization of 120?
(23)·3·5
Evaluate the product: (-4) * (-3) * (-2)
-24
On a square geoboard grid, Quadrilateral X has vertices at (0,0), (2,0), (2,4), and (0,4). Quadrilateral Y has vertices at (0,0), (5,0), (5,10), and (0,10). Are these figures similar, and why?
Yes, because
1. Their angles are the same (90 degrees) because they are both rectangles
2. The ratio of the corresponding sides is 2.5
Two similar rectangular fields have perimeters of 40 m and 120 m. If the area of the smaller field is 96 square meters, what is the area of the larger field?
864 m2
A flagpole casts a shadow of length 12 m on flat ground. At the exact same time, a 1.5 m tall student casts a shadow of length 2 m. Using Thales' theorem / similar triangles, how tall is the flagpole?
9m
Whats the GCD of 72 and 108?
36
What is the value of the expression |-15| - |-7| + (-4)?
4
In Triangle ABC, Angle A = 50° and Angle B = 70°. In Triangle PQR, Angle Q = 70° and Angle R = 60°. Are Triangle ABC and Triangle PQR similar?
Yes
A 3D cube has an edge length of 2 cm. A larger similar cube has an edge length of 6 cm. What is the ratio of the volume of the smaller cube to the volume of the larger cube?
1 to 27
In Triangle XYZ, line segment MN is drawn with M on XY and N on XZ such that MN is parallel to YZ. If XM = x + 1, MY = 4, XN = 6, and NZ = 8, what is the value of x?
x = 2
What's the LCM of 12, 18, and 20?
180
Evaluate the following multi-step expression following the order of operations:
(-3)2 - 4 * (-5) + (-12) / 3
25
On a geoboard, a polygon has a perimeter of 14 units. A second polygon is formed by multiplying all coordinates of the vertices of the first polygon by a scale factor of k = 3.5. What is the perimeter of the new polygon?
49 units
A scale model of a building is created using a scale of 1 : 50. If the model requires 0.2 liters of paint to cover its exterior surface, how many liters of paint would be needed to cover the exterior surface of the actual building?
500 L (0.2 · 502)
In Triangle ABC, DE is parallel to BC with D on AB and E on AC. If AD = x, DB = x + 3, AE = x - 1, and EC = x + 1, find the value of x.
x = 3
A gardener has 84 red roses, 105 white roses, and 126 yellow roses. She wants to make identical bouquets containing all three colors, with no flowers left over. What is the maximum number of identical bouquets she can make?
GCD(84, 105, 126) = 21
Simplify the nested integer expression:
-2 - [ -5 + 3 * (-4 - (-2)) ]
9