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
joja [24]
3 years ago
9

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC

by matching each mathematical statement with its reason.
*(select) = A, B, C, D, E, F, G, H, I, J

A. XY is perpendicular to AB.
B. XY ⊥ CD
C. m∠AXE = 90°, m∠DYE = 90°.
D. ∠AXE ≅ ∠DYE.
E. XE ≅ YE
F. ∠A ≅ ∠D
G. △AEX ≅ △DEY
H. AE ≅ DE
I. ∠AEB ≅ ∠DEC
J. △AEB ≅ △DEC

Statements:
(select) Definition of a perpendicular bisector
(select) ASA Triangle Congruence
(select) Definition of a midpoint
(select) In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
(select) Vertical Angles Theorem
(select) Definition of perpendicular lines
(select) Right angles are congruent.
(select) AAS Triangle Congruence
(select) Alternate Interior Angles Theorem
(select) Corresponding parts of congruent triangles are congruent.

Mathematics
1 answer:
Makovka662 [10]3 years ago
3 0

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

You might be interested in
Please help ASAP URGENT Will mark Brianlest
PIT_PIT [208]

Answer:

A

Step-by-step explanation:

i used the process of elimination and got rid of answers that didnt make sense but based on the info given i could tell that x was 5 months because of where the point of 5 is on the graph

8 0
3 years ago
Read 2 more answers
Which expression is equivalent to...? Screenshots attached. Please help! Thank you.
Studentka2010 [4]

Answer:

4x^{3} y^{2} (\sqrt[3]{4 x y})

Step-by-step explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }

Then we'll extract the 4 from the cubic root.  We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}

The answer is then:

4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})

4 0
2 years ago
4x = -36<br> plz helpppp
san4es73 [151]

Hi there! :)

4x=-36

Divide both sides by 4 in order to isolate x:

x=-9

Hope this helps you and have a nice day!

~Just a joyful teen

SilentNature

8 0
2 years ago
The graph of the even function F(X) Has 5 x-intercepts if (6,0) is the one of the intercepts what set of points can be the other
alex41 [277]

f(x) being even means


f(x) = f(-x)


So the zeros come in positive and negative pairs. If there are an odd number of intercepts like there are here, it's because one of them is x=0 which is its own negation.


Given zero x=6 we know x=-6 is also a zero.


So we know three zeros, and know the other two zeros are a positive and negative pair.


The only choice with (-6,0) and (0,0) is A.


Choice A



3 0
2 years ago
Read 2 more answers
Find the inverse function in slope-intercept form <br> f(x)=4/5x-16
jeka57 [31]
Y intercept slope - 5,0
X intercept slope - 0,-4
6 0
2 years ago
Other questions:
  • Find the volume of a rectangular prism with a length of 3 ¾ meters, a width of 1 ½ meters, and a height of 2 meters. A. 11.25 cu
    15·1 answer
  • Determine the mean, median, and more for the given data in each graph.
    15·1 answer
  • What’s the common greatest factor of 30 and 55
    12·2 answers
  • Cindy earns $10.50 per hour working at a restaurant. On Friday, she spent 1 3/4 hours cleaning, 2 1/3 hours doing paperwork, and
    11·1 answer
  • Can someone plz help me with this question
    8·1 answer
  • How many unique numbers can be made from creating a fraction with $2,3,4,$ or $6$ in the numerator and $2,3,4,$ or $6$ in the de
    7·2 answers
  • PLEASE HELP WILL GIVE BRAINLIEST, THANKS, AND STARS.
    5·1 answer
  • Write in slope intercept form an equation of the line that passes through the point (g,h) with slope j
    14·1 answer
  • A sample of 900 computer chips revealed that 58% of the chips fail in the first 1000 hours of their use. The company's promotion
    14·1 answer
  • You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!