Angles
What do complementary angles add up to?
90º
If point B is between points A and C, and AB = 5 and BC = 7, what is AC?
12 units
(by the Segment Addition Postulate)
A triangle has angle measures of 40°, 60°, and 80°. What type of triangle is it based on its angles?
Acute triangle
because all angles are less than 90°
What type of angle measures more than 90° but less than 180°?
Obtuse angle
What’s true about the slopes of two parallel lines in the coordinate plane?
They have the same slope
Two angles in a triangle measure 35° and 75°. What is the measure of the third angle?
70°
since 35 + 75 + x = 180 → x = 70
In ∠ABC, point D lies inside the angle. If m∠ABD = 30° and m∠DBC = 45°, what is m∠ABC?
75º
If AB = 12 and M is the midpoint, find AM.
AM = 6
A triangle has side lengths of 6 cm, 6 cm, and 10 cm. What type of triangle is it based on its sides?
Isosceles triangle
because two sides are congruent
Two angles form a linear pair. One measures 3x + 15°, and the other measures 5x – 3°. What is the value of x?
x = 21 because (3x + 15) + (5x – 3) = 180
Line m has the equation y = 2x + 1. What is the slope of a line perpendicular to m?
–½
because perpendicular lines have opposite reciprocal slopes
Can a triangle have side lengths of 4, 9, and 14? Why or why not?
No, because 4 + 9 = 13, which is not greater than 14
Two parallel lines are cut by a transversal. If one corresponding angle is 65°, what is the measure of all corresponding angles?
65º
(corresponding angles are congruent)
Point M is between A and B. AM = 2x + 1, MB = x + 5, and AB = 17. Find x.
x = 3
because 2x + 1 + x + 5 = 17
A right triangle has one leg that measures 6 units and a hypotenuse of 10 units.
What is the length of the other leg? Give your answer in simplified radical form.
8 units
x^2+6^2=10^2
x^2 = 64