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
dusya [7]
3 years ago
6

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC so t

he alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?

Mathematics
2 answers:
rewona [7]3 years ago
8 0

Answer:

SAS rule

Step-by-step explanation:

To prove: A quadrilateral ABCD is a parallelogram.

Proof: It is given that ABCD is an equilateral, thus side AB is parallel to side DC so the alternate interior angles are congruent, thus ∠ABD and ∠BDC, are congruent.

Also, From ΔADB and ΔCDB, we have

AB=DC (Given)

∠ABD =∠BDC (Alternate angles)

DB=DB (Common)

Thus, by SAS rule of congruency, ΔADB is congruent to ΔCDB that is ΔADB≅ΔCDB.

By CPCTC, ∠DBC and ∠ADB are congruent and sides AD and BC are congruent. ∠DBC and ∠ADB form a pair of alternate interior angles.

Therefore, AD is congruent and parallel to BC.

Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Hence proved.

Nana76 [90]3 years ago
5 0
<span>Therefore, the triangles ABD and CDB are congruent by SAS</span>
You might be interested in
Taylor got an Ulta gift card that had $20 on it. If she bought 3 lipsticks at $2.99 each
Vadim26 [7]

$6.44 is left

Hope this helps! :D

4 0
3 years ago
Read 2 more answers
Grace earns $7 for each car she washes. She always saves $25 of her weekly earnings.This week,she wants to have at least $65 in
Irina-Kira [14]

Answer:

she must wash 8 cars because 7 x 8 = 56 so yeah bye

Step-by-step explanation:


7 0
3 years ago
I need help :) please if you know this I would appreciate it if you can help me
elena-14-01-66 [18.8K]

Step-by-step explanation:

a.

2(3x) - 5x = 4

6x - 5x = 4

x = 4

B. -5(x-4)+8x=29

-5x+20+8x=29

3x+20=29

3x=9

x=3

C. 2y=18+2(3-y)

2y=18+6-2y

2y=24-2y

4y=24

y=6

D. c = -b - 11

3c + 6 = 6b

3( -b - 11) +6 = 6b

-3b-33+6=6b

-3b-27=6b

-27=9b

3=b

3 0
2 years ago
Fill in the [?]:<br> 11,562 um = [?]m<br> Give your answer in standard form.<br> Enter
Vitek1552 [10]
Divide the number by 1,000,000 (1 million).

Micrometer is a millionth of a meter

11,562/1,000,000 = 0.011562
6 0
2 years ago
Find the distance (-4,6) and (3,-7)
forsale [732]

Answer:

Distance ≈ 14.8

Step-by-step explanation:

<u>Calculate the distance (d) using the distance formula</u>

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, 6) and (x₂, y₂ ) = (3, - 7)

Hope this helps!!!!

3 0
3 years ago
Other questions:
  • Help me please in part “A” and part “B”
    6·1 answer
  • Naomi has a neon tretra fish
    13·1 answer
  • What's 5/6 of a gallon?
    6·1 answer
  • Use the unit circle to find the inverse function value in degrees.
    11·1 answer
  • The lengths of the sides of a triangle are 6, 8, 10. Can the triangle be a right triangle? Yes or no?
    13·1 answer
  • Seven less than the product of a number n and 1/6 is no more than 94
    8·1 answer
  • PLS HELP OMG ITS ALGEBRA 1 im gonna drop out at this point
    6·1 answer
  • I need help plsssssss
    5·1 answer
  • If a train travels at 80 mph for 12 min, what is the distance traveled?
    8·2 answers
  • HELP!! I need this for tonight :(
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!