Reasons used in Proofs
Define a perpendicular bisector
What is a segment that splits a segment into two congruent segments and forms 2 congruent right angles.
A parallelogram must be a rhombus if its diagonals are __________.
What is perpendicular
Bob places an 18-foot ladder 6 feet from the base of his house and leans it up against the side of his house. Find, to the nearest degree, the measure of the angle the bottom of the ladder makes with the ground.
What is 71 degrees.
DAILY DOUBLE !!!!!!!
Line segment NY has endpoints N(-11,5) and Y(5,-7). What is the equation of the perpendicular bisector of NY ?
What is y+1=(4/3)(x+3) or y=(4/3)x +3
What is the minimum rotation about its center that will carry a regular decagon onto itself?
What is 36 degrees
What does CPCTC stand for?
What is Corresponding Parts of Congruent Triangles are Congruent.
What are the defining characteristics of a rhombus
What is all sides are equal, diagonals are perpendicular to each other, and diagonals bisect the angles at which they are drawn.
In right triangle ABC, m∠A = 32°, m∠B = 90°, and AC 6.2 cm. What is the length of BC , to the nearest tenth of a centimeter?
What is 3.3
Point Q is on MN such that MQ:QN = 2:3. If M has coordinates (3,5) and N has coordinates (8, -5), the coordinates of Q are
What is (5, 1)
Determine and state, in terms of π, the area of a sector that intercepts a 40° arc of a circle with a radius of 4.5.
What is 2.25π
What are the ways to prove triangles congruent and the ways to prove triangles similar?
What is SSS, SAS, ASA, SAA, HL (right triangles only)
AA, SSS, SAS
In square ABCD, the measure, in inches, of AB is 3x + 2 and BC is x + 12. Find the number of inches in the length of DC
What is 17.
In a right triangle, sin (40 - x)° = cos (3x)°. What is the value of x?
What is 25.
What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x - 6y =15?
What is y=-(3/2)x + 18
The equation of a circle is x2 + y2 - 6y + 1 = 0. What are the coordinates of the center and the length of the radius of this circle?
What is (0, 3) and radius of 2sqrt2
Define an altitude of a triangle
What is a segment that extends from a vertex of a triangle perpendicular to opposite side, the height of a triangle.
Rhombus ABCD has coordinates A(0,7) and C(2,l). What is the slope of diagonal BD?
What is 1/3
A 13 foot ladder is placed 5 feet away from the foot of a wall. Determine how far up the wall the ladder will reach.
What is 12 feet.
In the coordinate plane, the vertices of triangle PAT are P(1,6), A(4,5), and T(5,2). Prove that PAT is an isosceles triangle.
What is, PAT is an isosceles triangles because sides AP and AT are congruent.
A water cup in the shape of a cone has a height of 4 inches and a maximum diameter of 3 inches. What is the volume of the water in the cup, to the nearest tenth of a cubic inch, when the cup is filled to half its height?
What is 1.2 inches3
When a segment or an angle is congruent to itself
What is the Reflexive property
The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3), and V(-5,7). What is the perimeter of RSTV?
What is 4 sqrt 20
In right triangle RST with <S=90, altitude SU is drawn to RT at U. UT = 12, and RT = 42, Determine the length of SU, in simplest radical form
What is 6sqrt10
Quadrilateral PQRS has vertices P(-2,3), Q(3,8), R(4,1), and S(-1,-4). Prove that PQRS is a rhombus.
What is 4 congruent sides d = sqrt50
In circle 0, secants ADB and AEC are drawn from external point A such that points D, B, E, and Care on circle 0. If AD= 8, AE = 6, and EC is 12 more than BD, the length of BD is
What is 22.