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Figure ABCD is a rhombus. If m<DAB=144+x, and m<ADC=x, then what is the measure of <ADC?

STEP 1: Rhombus' consecutive angles add up to 180, therefore we can say that 144+x+x=180.

STEP 2: Now solve. Combine the x's to make 144+2x=180. Now subtract 144 from 180 to get 2x=36. Divide 2 on both sides of the equation and we get x=18.

STEP 3: The question asks to find the m<ADC, which is x. Since we found the value of x, we know that m<ADC=18.

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Figure ABCD is a rectangle. If m<A=15x+15 find the value of x.

STEP 1: Considering the characteristics of a rectangle, we can conclude that all angles are equal to 90 degrees. Including <A. Therefore, we can create an equation: 15x+15=90.

STEP 2: Now solve. Subtract 15 from both sides. This leaves us with 15x=75. Now divide 15 by both sides, giving us the answer of x=5.

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Figure ABCD is an isosceles trapezoid with mid segment EF. If base DC=8 and base AB=12, what is the length of EF?

STEP 1: Knowing that EF is a mid segment, we can use Theorem 6-16 to set up an equation. The equation would be EF= 1/2 (8+12).

STEP 2: Now solve it. First we distribute the 1/2, leaving us with EF= 4+6. Add 4 and 6 to get EF

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A quadrilateral is a parallelogram if  any one of the following is true:

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A quadrilateral is a parallelogram if  any one of the following is true:

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1. Both pairs of opposite sides are parallel (Definition)

2. Both pairs of opposite sides are congruent (THM 6-5)

3. Both pairs of opposite angles are congruent (THM 6-6)

4. Diagonals bisect each other (THM 6-7)

5. A pair of opposite sides is both parallel and congruent

(THM 6-8)

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Figure ABCD is a square. Given that side AB=3x+1, and side DC=31, find the value of x.

STEP 1: Knowing the characteristics of a square, we know that all sides are congruent. So this means that we can set the sides equal to each other.

STEP 2: Solve the equation

3x+1=31

Subtract 1 from both sides, which leaves you with 3x=30. Then divide 3 by both sides, giving you x=10.

There's our answer

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True or false: Consecutive angles of a rhombus are congruent ?

ANSWER: false

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6-1 THM: opposite sides of a parallelogram are congruent

6-2 THM: opposite angles of a parallelogram are conruent

6-3 THM: consecutive angles in a parallelogram are supplementary

6-4 THM: the diagonals of a parallelogram bisect each other

6-5 THM: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

6-6 THM: if both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

6-7 THM: if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

6-8 THM: if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram

6-9 THM: if a parallelogram is a rectangle, then its then its diagonals are congruent

6-10 THM: if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

6-11 THM: the diagonals of a rhombus are perpendicular

6-12 THM: if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

6-13 THM: each diagonal of a rhombus bisects a pair of opposite angles

6-14 THM: both pairs of base angles of an isosceles trapezoid are congruent

6-15 THM: the diagonals of an isosceles trapezoid are congruent

6-16 THM: the median of a trapezoid is parallel to the bases , and its measure is one half the sum of the measures of the base

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QUADRILATERAL: a four-sided polygon

PARALLELOGRAM: a quadrilateral with both pairs opposite side parallel

PROBABILITY: the ratio of the number of favorable outcomes to the number of possible outcomes

RECTANGLE: quadrilateral with four right angles

RHOMBUS: a quadrilateral with four congruent sides

TRAPEZOID: a quadrilateral with exactly one pair of parallel sides

BASES OF A TRAPEZOID: two parallel sides in a trapezoid

LEGS: two nonparallel sides in a trapezoid

BASE ANGLES OF A TRAPEZOID: angles formed by one base and one leg

ISOSCELES TRAPEZOID: trapezoid with congruent legs