Geometric Mean
Quadrilaterals
Pythagorean Theorem
Similarity
Right Triangles and Trigonometry
100
This theorem states that in the image below
Δ BAC ~ Δ BCD ~ Δ CAD
What is the Right Triangle Altitude Theorem
100
What is the name for a quadrilateral with both pairs of opposite sides parallel?
A parallelogram
100
What is the name of the set of positive integers that satisfy the equation below:
a2 + b2 = c2
They are called Pythagorean triples
100
What are 3 similarity criteria for any two triangles?
AAA (or AA), SSS, SAS, ASA, AAS
100
The three basic trigonometric ratios and the pneumonic device we use to remember them
What are sine, cosine, and tangent and SOH CAH TOA
200
What is the name of the formula below:
A/X = X/B
Geometric mean formula
200
In the image below, find the value of x. Explain any theorems you used.
x is equal to 4. A theorem states that the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.
200
Give two pairs of common Pythagorean Triples
3,4,5 and 5,12,13
200
What are the two similarity criteria for right triangles?
HL (hypothenuse-leg) and AL (acute angle-leg)
200
What is the name given to triangles whose angle measures are 45-45-90 or 30-60-90
Special right triangles
300
In the image below, find the length of CD. Explain any theorems or rules you used.
CD has a length of 4. The right triangle altitude theorem is used.
300
The sides of parallelogram ABCD are represented in the image below. Find the length of DA and state any rules or properties that were used.
DA has a length of 24. The opposite sides of a parallelogram are congruent.
300
What is the length of the diagonal in the rectangle below? (Round to two decimal places)
The length of x is 40.25 meters.
300
In the image below, are the two triangles similar?
If they are similar, what similarity criteria is used?
If they are similar, also find the length of side PQ and side RP.
ΔABC and ΔPQR are similar by AA.
Side PQ has a length of 8 and side RP has a length of 14.
300
In the image below, the value of f and e
What is 26 divided by the square root of 2?
400
In the image below, find the value of x. Explain any theorems or rules you used.
x has a value of 9. The leg rule was used.
400
In the image below, find the measure of ∠F in the parallelogram DEFG and state any rules or properties that were used.
The measure of ∠F is 60 degrees. In parallelograms, consecutive angles are supplementary.
400
A soccer field is rectangle 90 meters wide and 120 meters long. The coach tells the players to run from one corner to the corner diagonally across the field. How far do the players have to run?
The players must run 150 meters.
400
In the image below, find the value of x. Explain any theorems or rules you used.
The two triangles are similar by AAA (or AA). x has a value of 7.2 cm.
400
In the image below, what are the values of x and y?
x is 12 divided by the square root of 3
y is 24 divided by the square root of 3
500
In right triangle ΔABC, ∠C is a right angle. CD, the altitude to the hypotenuse, has a length of 8 units. If the segments of the hypotenuse are in the ratio of 1 : 4, find the number of units in the two segments of the hypotenuse. Sketch a figure and explain any theorems or rules you used.
The segments have 4 and 16 units. The right triangle altitude theorem was used.
500
In the image below the isosceles trapezoid BEAR is shown. Find the length of AQ.
AQ has a length of 8.
500
Jill's front door is 42 inches wide and 84 inches tall. She recently purchased a circular table with a radius of 48 inches. Will the table fit through the door? Explain.
No, the table is about 2 inches too small because the diagonal of the door is only 93.91 inches and the diameter of the table is 96.
500
In the image below, find the value of x. Explain any theorems or rules you used.
The two triangles are similar by ASA or AAA. x has a value of 17.5 cm.
500
In the image below, find the measure of ∠A and the lengths of side AC and side BC
∠A is 38 degrees
Side AC is 15.23
Side BC is 9.38