Transformations
A rectangle is reflected across the y-axis. If one of its original vertices is (−3,5), what are the coordinates of its corresponding reflected point?
(3,5)
What is the ratio of the opposite side to the hypotenuse in a right triangle called?
Sin
If x = 5 and y = x-4, what is the value of y?
1
What is the term for triangles that have the same shape but different sizes?
Similar Triangles
A function f(x) is transformed into g(x)=f(x−3)+2. Describe the transformations that have been applied to f(x).
3 units right, 2 units up
In a right triangle, if the adjacent side is 5 units and the hypotenuse is 13 units, what is the cosine of the angle?
5/13
Which property of equality justifies the following statement?
a = b, then b = a
Symmetric property of equality
Two triangles are similar, and the ratio of their corresponding sides is 5:7. If the area of the smaller triangle is 25 square units, what is the area of the larger triangle?
49 square units
A triangle has vertices at (2,3), (5,7), and (6,4). If the triangle is translated 4 units to the right and 2 units down, what are the coordinates of the new vertices?
(6,1), (9,5), (10,2)
In triangle ABCABCABC, if ∠A=30, side a=8, and side b=12, what is the sine of angle B?
sinB = 0.75
Given the following statement ∠A=∠B, ∠B=∠C, and C=8, find the value of A and the relationship between A and C.
A=8, transitive property of equality
What is the congruence called when two triangles are congruent if two sides and the included angle are equal?
SAS (Side-Angle-Side) congruence
A square undergoes a dilation with a scale factor of 2 centered at the origin. If one of its original vertices is at (3,−1), what are the coordinates of its new image?
(6,−2)
Given a triangle with angles A=40, B=60, and side a=10, find the length of side b using the Law of Sines.
b≈13.47
if 2x-4y = 12, and y = 3, determine the property of equality that is used and the value of x.
substitution property of equality, x=12
If two triangles are similar, and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?
4:9
A point P(4,−2) is rotated 90° counterclockwise around the origin. What are the new coordinates of point P?
(2,4)
In a non-right triangle, if ∠A=25°, ∠B=95°, and side c=18, find the length of side a using the Law of Sines.
a≈7.63
Triangle ABC and DEF are similar. The corresponding sides of the triangle measure (ABC to DEF) 2:3. If triangle ABC has a height of 18, and triangle DEF has a base of 12, determine the height, base, and area of triangle ABC and DEF.
ABC: height:18, base:8 area:72.
DEF: height:27 base:12 area:162
Two triangles are similar, and the ratio of their corresponding sides is 4:5. If the area of the smaller triangle is 36 square centimeters, what is the area of the larger triangle?
56.25cm2