Category 1
What is a characteristic of a parallelogram?
Opposite sides are equal and parallel.
What are the conditions that make a quadrilateral a parallelogram?
Opposite sides are equal, opposite angles are equal, or the diagonals bisect each other.
If two pairs of opposite sides are equal, what can be concluded?
The quadrilateral is a parallelogram.
What can be said if both pairs of opposite angles are equal?
The quadrilateral is a parallelogram.
If the diagonals bisect each other, what type of quadrilateral is it?
It is a parallelogram.
What is the sum of the interior angles of a parallelogram?
360°
If the length of side AB is 8, what is the length of the side CD?
8 (because opposite sides are equal).
What are the opposite angles in a parallelogram?
They are equal.
If angle A = 70°, what is angle C?
70° (because opposite angles are equal).
If side AB = 10 and BC = 5, what is the length of AD?
10 (because opposite sides are equal).
What is a rectangle?
A parallelogram with four right angles.
What defines a rhombus?
A parallelogram with all sides equal.
How is a square different from a rectangle?
A square has all sides equal and all angles are right angles.
What theorem can be used to prove a quadrilateral is a rectangle?
The diagonals are equal.
What properties do kites share with parallelograms?
Kites have equal adjacent sides and one pair of opposite angles are equal
What does the Midline Theorem state?
The midline of a trapezoid is parallel to the bases and its length is the average of the lengths of the bases.
If the midline is 8, what is the length of the base?
The sum of the bases divided by 2 equals 8.
How can the Midline Theorem help in solving trapezoid problems?
It provides a way to find relationships between the bases and the midline.
If the legs of a trapezoid are 10 and 14, what is the length of the midline?
It is the average of the two bases.
What is the relationship between the midline and the parallel bases?
The midline is half the sum of the lengths of the bases.
What is a proportion?
An equation stating that two ratios are equal.
A class has boys and girls in the ratio of 4:3. If there are 28 boys, how many girls are there?
Answer:
4/3 = 28/g
4g=28(3)
4g =84
4g ÷ 4 = 84 ÷ 4
g = 21
In a fruit basket, the ratio of apples to bananas is 2:5. If there are 10 apples, how many bananas are there?
2/5 = 10/a
2a = 10(5)
2a = 50
2a ÷2 = 50 ÷2
a = 25
If 4/8 = x/16, what is x?
8
How do you write a proportion from two ratios?
By setting the cross products equal to each other.