10. Which of the following quadrilaterals always have diagonals that are congruent. Circle all that apply
Parallelograms
Rectangles
Rhombi
Squares
Isosceles trapezoids
19. Given square ABCD: if the measure of angle ACB = (1x - 32) degrees, find the value of x. Round to the nearest tenth
17. Given rhombus DEFG: if GE = 42 and DH = 16, find GF
20. WXZY is a quadrilateral with W locates at (-5, 2) and Xoxated at (3, 0). What must be the slope of segment ZY in order for WXYZ to be a parallelogram
Man, you need to brush up on your geometry before providing answers.
10. The only ones that have congruent diagonals are
Rectangles
Squares (since they are rectangles!)
Isosceles trapezoids
Draw some of the others and it is easy to see they do not qualify
19. The diagonals of a square bisect the corner angles. Thus, angle ACB is 45 degrees.
So, set
1x-32 = 45
x = 77
I suspect a typo because
(a) the result is an integer, so no rounding needed
(b) who says "1x" ?
17.
DH? Where is H? If you meant DF=16, then since the diagonals are perpendicular, you have 4 congruent right triangles with sides 21 and 8. GF is the hypotenuse of one of these, with length
√(8^2+21^2) = √505 = 22.47
20.
WX has slope (0-2)/(3+5) = -1/4
YZ must also have that slope, if it is parallel
But that will not necessarily make it a parallelogram, unless its length is also that of WX.
10. The quadrilaterals that always have congruent diagonals are rectangles, rhombi, and squares.
19. To find the value of x, we need to solve the equation: measure of angle ACB = (1x - 32). Since we know that ABCD is a square, all angles are right angles, which means ACB is also 90 degrees. So we set up the equation: 90 = 1x - 32. Solving for x, we have: 1x = 90 + 32, 1x = 122, x = 122. Therefore, the value of x is 122.
17. In a rhombus, opposite sides are congruent. Therefore, GE is congruent to FH and DG is congruent to EH. Since GE = 42 and DH = 16, we know that GF is also 42 and HF is also 16.
20. In order for WXYZ to be a parallelogram, opposite sides must be parallel. The slope of a line is given by the formula: m = (y2 - y1) / (x2 - x1). Segment WX has coordinates (-5, 2) and (3, 0). The slope of WX is (0 - 2) / (3 - (-5)) = -2 / 8 = -1/4. To make segment ZY parallel to WX, it must have the same slope. Therefore, the slope of segment ZY must also be -1/4.
10. To determine which of the quadrilaterals have congruent diagonals, we need to understand the properties of each shape.
- Parallelograms have opposite sides that are parallel and congruent, but their diagonals are not necessarily congruent.
- Rectangles have all angles measuring 90 degrees, which implies that their diagonals are congruent. So rectangles have diagonals that are always congruent.
- Rhombi have all sides congruent, but their diagonals are not necessarily congruent.
- Squares are a special type of rectangle and rhombus, meaning they have all the properties of both rectangles and rhombi. Therefore, squares have diagonals that are always congruent.
- Isosceles trapezoids generally don't have congruent diagonals.
Based on these properties, the quadrilaterals that always have congruent diagonals are rectangles and squares. So you should circle "Rectangles" and "Squares" as the correct answers.
19. In square ABCD, we are given that the measure of angle ACB is (1x - 32) degrees. To find the value of x, we need to set up an equation.
Since all angles in a square are 90 degrees, we know that angle ACB must also measure 90 degrees. Therefore, we can write the equation:
1x - 32 = 90
Now, let's solve for x:
1x = 90 + 32
1x = 122
x = 122
So the value of x is 122. Rounded to the nearest tenth, x ≈ 122.
17. In rhombus DEFG, we are given that GE = 42 and DH = 16. To find GF, we can first draw a diagram of the rhombus:
D------+-------C
|\ |
| \ |
| \ |
| \ |
| \ |
E--------F
Since all sides of a rhombus are congruent, we know that GE = ED = GF = FC = 42. Therefore, we can conclude that GF = 42.
So GF is equal to 42 units.
20. In quadrilateral WXYZ, we are given that W is located at (-5, 2) and X is located at (3, 0). To determine the slope of segment ZY that would make WXYZ a parallelogram, we need to consider the properties of parallelograms.
In a parallelogram, opposite sides are parallel, so they have the same slope. To find the slope of segment ZY, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of Z and Y, let's calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (0 - 2) / (3 - (-5))
m = -2 / 8
m = -1/4
Therefore, the slope of segment ZY must be -1/4 for WXYZ to be a parallelogram.
10. Rhombuses are like squares but with diagonal parallel lines. Parallelograms are like rectangles with diagonal parallel lines. Which one?
19. Set the measure to zero.
1x - 32 = 0
1x -32 +32= 0+32
1x /1 = 32 /1
x = ??
17. I'm not 100% sure how to do this one.
20. Find the slope of WX. Slope formula: (y^2-y^1)/(x^2-x^1)
(0-2)/(3-(-5))
??/??