Parallel & Perpendicular Lines
What is it called when a line intersects two parallel lines?
A transversal
What kind of transformation flips a figure over a line?
Reflection
What is the triangle congruence in which two triangles have two pairs of congruent sides and the included angle in one triangle is congruent to the included angle in the other triangle?
SAS
Two triangles that have two pairs of congruent angles are similar by what theorem?
Angle Angle Similarity
8 + 2 ⋅ (6 - 4)3 ÷ 4
12
The ________ of lines can determine if two lines are parallel, perpendicular, or neither.
Slope
A triangle with vertices at A(2,3), B(4,5), and C(6,7) is reflected over the x-axis. What are the new coordinates of the vertices?
A'(2,-3), B'(4,-5), C'(6,-7)
What are the three transformations that can prove triangle congruence?
Translations, reflections, and rotations.
Triangle ABC has side lengths, AB=3, BC=5, and AC=6. Triangle DEF has sides lengths DE=9, EF=15, and DF=19. Are triangles ABC and DEF similar?
No
36 ÷ 6 + 4 ⋅ (3+2) - 52
1
When two parallel lines are cut by a transversal, what angles are congruent?
Corresponding angles
If the point (-3,7) gets rotated 180° around the origin, what is its new coordinate?
(3,-7)
Name two characteristics of an isosceles triangle.
In a similar triangle, one side is 8 cm, and its corresponding side in another triangle is 12 cm. What is the scale factor?
2/3 or 3/2
4 + 3 ⋅ 23 - 10 ÷ 2
23
Write an equation of a line that is parallel to the line y=3x-5 and passes through the point (1,4).
y-4=3(x-1) or y=3x+1
The triangle ABC, with vertices A(-3,1), B(2,4), and C(5,-2) gets dilated by a factor of 3, what are the vertices of triangle A'B'C'?
A'(-9,3), B'(6,12), C'(15,-6)
If triangle ABC can be translated 5 units up, 2 units down, and dilated by a factor of 2 in order to line up with triangle DEF, are triangle ABC and DEF congruent?
No
Two right triangles are similar. One triangle has side lengths of 4 cm, 6 cm, and 8 cm. What are the corresponding side lengths of the other triangle if the scale factor is 3?
12 cm, 18 cm, and 24 cm
(2 + 3)2 ÷ 5 + 23 - 7
6
Write an equation of a line that is perpendicular to y=4x+3 and passes through the point (4,2).
y-2=-(1/4)(x-4) or y=-(1/4)x+3
The rectangle ABCD has vertices A(-4,2), B(2,2), C(2, -1) and D(-4,-1). If rectangle ABCD gets reflected over the line y=-2 and translated 4 units to the right, what are the coordinates of rectangle A'B'C'D'?
A'(0,-6), B'(6,-6), C'(6,-3), D'(0,-3)
True or false: AAA can prove triangle congruence.
False!
A 6 ft tall person casts a shadow that is 4 ft long. A tree casts a shadow that is 10 ft long. Using similarity, what is the height of the tree?
15 ft
15 - [2 (6 + 3) - 5] + 42
18