1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inn [45]
3 years ago
11

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Mathematics
1 answer:
Irina-Kira [14]3 years ago
3 0

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

<h3>1.</h3>

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322}  \\VX \approx 36.36

Also, YW \approx 36.36, beacuse rectangles have congruent diagonals, which intercect equally.

That means, ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18

<h3>2.</h3>

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\  DG \approx 25.75

<h3>3.</h3>

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

\angle 4  = 31\°

Which means \angle 3 = 59\°, beacuse it's the complement for angle 4.

Now, \angle 6 = 59\°, because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

\angle 9=180-59-59=62, by interior angles theorem.

\angle 8 =62, by vertical angles theorem.

\angle 10 = 180- \angle 9=180-62=118\°, by supplementary angles.

\angle 7 = 118\°, by vertical angles theorem.

\angle 5=90-59=31, by complementary angles.

\angle 2 = \angle 5 = 31\°, by alternate interior angles.

\angle 1 = 59\°, by complementary angles.

<h3>4.</h3>

m\angle BCD=90\°, because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

m\angle ABD = 6\° = m\angle BDC, by alternate interior angles and by given.m\angle CBE=90-6=84, by complementary angles.

m\angle ADE=90-6=84, by complementary angles.

m\angle AEB=180-6-6=168\°, by interior angles theorem.

m\angle DEA=180-168=12, by supplementary angles.

<h3>5.</h3>

m\angle JMK=180-126=54, by supplementary angles.

m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63, by interior angles theorem, and by isosceles triangle theorem.

m\angle HLK=90\°, by definition of rectangle.

m\angle HJL=\frac{180-126}{2}=27, by interior angles theorem, and by isosceles triangle theorem.

m\angle LHK=90-27=63, by complementary angles.

m\angle = JLK= m\angle HJL=27, by alternate interior angles.

<h3>6.</h3>

The figure is a rectangle, which means its opposite sides are equal, so

WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5

Then, we replace this value in the expression of side WZ

WZ=7x-6=7(5)-6=35-6=29

Therefore, side WZ is 29 units long.

<h3>7.</h3>

We know that the diagonals of a rectangle are congruent, so

SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9

Then,

PR=5x+28=5(9)+28=45+28=73

Therefore, side PR is 73 units long.

You might be interested in
15.00 + 1.75x &gt; 7.50 + 2.25
ElenaW [278]

Answer:

Step-by-step explanation:

7 0
3 years ago
Can someone answer this question please answer it correctly and show work please
GenaCL600 [577]

Answer:

5) C pink   6) A -1/2x + 1/4     7) D z ≥ 0

Step-by-step explanation:

5) White 1/6 = 4/24

  Green  1/3 = 8/24

  Pink 1/8 = 3/24

  Yellow 3/8 = 9/24

6) 11/2x - 2(3x - 1/8)       Distribute the -2

   11/2x - 6x + 1/4           Combine like terms

-1/2x + 1/4

7) z ≥ 0

z is greater than or equal to 0

8 0
3 years ago
Read 2 more answers
-3s = -24 what does S equal
qaws [65]
-3s=-24 to find s you will divide both sides by -3
S=8
8 0
3 years ago
Read 2 more answers
About how long is each side of a square that is 125 square miles
stiv31 [10]
Square = identical sides.
therefore, 125miles^2 = (square root 125)^2

square root 125 = 11.18033989miles
5 0
3 years ago
Kyle drives his truck 429 miles on 33 gallons of gas. How many miles can Kyle drive on 1 gallon of gas?
expeople1 [14]
Ratio and proportion

429 mi/33 gallon= x miles/ 1 gallon

cross multiply

33x= 429

x=13 miles on one gallon

hope this helps

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is 77/200 in decimal form. How to work it out
    7·2 answers
  • How do you set this up?
    7·1 answer
  • 10 students are standing equidistant from the center of a classroom. they are all holding hands to begin with. they must go and
    10·2 answers
  • I need help please?!!!!
    10·1 answer
  • the length of a rectangle is 4 feet more than its width. The area of the rectangle is 60ft^2. Find the length and width of the r
    12·1 answer
  • The standard form of the equation of a parabola is x = y2 - 4y + 20. What is the vertex form of the equation? A.x = (y - 4)2 + 1
    10·1 answer
  • The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard d
    7·1 answer
  • What is the volume?<br>h<br>12 cm<br>Round your answer to the nearest tenths:​
    9·1 answer
  • Please helppppp Is this correct
    9·1 answer
  • Can someone please explain this
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!