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
Marina86 [1]
3 years ago
12

Figure ABCD is a parallelogram.

Mathematics
2 answers:
Sonbull [250]3 years ago
7 0
Answer is

A. First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles.

hope it helps
lutik1710 [3]3 years ago
5 0

Answer:

Option A is correct.

First prove ABC is congruent to CDA and then state AD and BC are corresponding sides of the triangles.

Step-by-step explanation:

Given the figure: ABCD is a parallelogram.

Parallelogram states that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

therefore, AB is parallel to CD    [by definition of parallelogram]

here, in the figure, AC becomes a transversal line.

let \triangle CDA and \triangle ABC

Alternate angle property states that the two angles are on opposite sides of the sloping transversal line.

\angle DAC = \angle BCA  [Angle]     [By property of alternate angle]

AC = AC       [Common side]

\angle ACD = \angle BAC  [Angle]       [By property of alternate angle]

ASA (Angle-Side-Angle) Postulates states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

therefore, by ASA postulates;

\triangle CDA \cong \triangle ABC

Then, by CPCT [ Corresponding part of the congruent triangle]

AD = BC         hence proved!

You might be interested in
Solve for x: 2x^5/3-22=464 a) x = 28 b) x = 27 c) x = ±27 d) x = ±28
Effectus [21]

Answer:

<h3>x = 27</h3>

Step-by-step explanation:

Given the expression {2x^{\frac{5}{3} }-22 = 464, we are to find the value of x in the expression. This is as shown below;

{2x^{\frac{5}{3} }-22 = 464

add 22 to both sides

{2x^{\frac{5}{3} }-22 = 464+22\\\\

{2x^{5/3} =486

divide both sides by 2

\frac{2x^{5/3}}{2} =\frac{486}{2}\\ x^{5/3} = 243

raise both sides to the power of 3/5

(x^{5/3})^{3/5} = (243)^{3/5}\\x = (\sqrt[5]{243}) ^3\\x = 3^3\\x = 27

Hence the value of x is 27

8 0
3 years ago
It’s a test question.
marissa [1.9K]

Answer:

A # is odd

Step-by-step explanation:

Hypothesis-----> conclusion

4 0
3 years ago
Brett is 75 feet from the base of a building. he measures the angle of elevation to the top of the building and records it as 80
SashulF [63]
This is the concept of trigonometry, we are required to calculate the number of floors the building has given the information above;
# floors=[height of the building]/[height of each floor]
height of each floor=17 ft
let the height of the building be,h.
h is given by;
tan theta=opposite/adjacent
theta=80
opposite=h
adjacent=75 ft
thus
tan 80=h/75
h=75 tan 80
h=425.35 ft
thus the number of floors will be:
425.35/17
=25.020≈25 floors


8 0
3 years ago
The sum of a number (n) and 14 is 72. Which equation shows this relationship
NemiM [27]
I believe the answer is N+14=72
6 0
3 years ago
Read 2 more answers
What is the slope of the line (1/2,-4) (1/2,5)
soldi70 [24.7K]
It’s says error Bc u can’t do 9/0
7 0
3 years ago
Other questions:
  • Solve for x. 4x − 3/ 3 =7 Enter your answer in the box. x =
    9·2 answers
  • A parallelogram with a base of x units and a height of y units is changed
    9·1 answer
  • PLS HELP ILL MARK AS MY BRAINLESS
    13·1 answer
  • Find the value for x:
    5·2 answers
  • Explain how to find the surface area of rectangular prisms and cubes. What formulas can you use?
    14·2 answers
  • Line C passes through points (0, 2) and (8,8). What is the slope of a line parallel to line C?
    14·1 answer
  • Solve the system of equations. If the system does not have one unique solution, determine the number of solutions to the system.
    13·1 answer
  • PLEASE HELP ASAP- What is the value of AB?
    11·1 answer
  • A taxi cab costs $3.75 for the first mile and $0.85 for each additional mile. You
    7·1 answer
  • Use substitution to solve this problem<br>a=5, b=2<br>5a - b = ‽<br>​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!