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
vladimir2022 [97]
2 years ago
11

Given that ∠FAB≅∠GED and C is the midpoint of AE¯¯¯¯¯, which of the following proves that △ABC≅△EDC?

Mathematics
1 answer:
qwelly [4]2 years ago
3 0

Step-by-step explanation:

Use one of the triangle congruence theorems (SAS, SSS, ASA, AAS, or HL) to prove that △ABC≅△EDC

.

It is given that  ∠FAB≅∠GED

. ∠BAC is the supplement of ∠FAB, and ∠DEC is the supplementary of ∠GED

by the definition of supplementary angles.

The figure shows the same triangles A B C and C D E as in the beginning of the task. Angle B A C is highlighted in green. Angle D E C is highlighted in blue.

Notice that ∠BAC

and ∠DEC are supplemental to congruent angles ∠FAB and ∠GED respectively. The Congruent Supplements Theorem states that if two angles are supplementary to two congruent angles, then the two angles are congruent. Therefore, ∠BAC≅∠DEC

by the Congruent Supplements Theorem.

The figure shows the same triangles A B C and C D E as in the previous figure. Angles B A C and D E C are congruent and highlighted in blue.

Notice that ∠ACB

and ∠ECD are vertical angles. The Vertical Angles Theorem states that vertical angles are congruent.

Therefore, ∠ACB≅∠ECD

by the Vertical Angles Theorem.

The figure shows the same triangles A B C and C D E as in the previous figure. Angles B C A and D C E are congruent and highlighted in red.

It is also given that C

is the midpoint of AE⎯⎯⎯⎯⎯

.

By the definition of midpoint, AC⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯

.

The figure shows the same triangles A B C and C D E as in the previous figure. Sides A C and C E are congruent and highlighted in red.

So, two pairs of corresponding angles in △ABC

and △EDC are congruent, and the included sides in △ABC and △EDC

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

Therefore, △ABC≅△EDC

by ASA.

Translate these seven statements and reasons into a 2-column proof.

1. ∠FAB≅∠GED

(Given)

2. ∠BAC

is the supp. of ∠FAB; ∠DEC is the supp. of ∠GED (Def. of Supp. ∠

s)

3. ∠BAC≅∠DEC

(≅

Supp. Thm.)

4. ∠ACB≅∠DCE

(Vert. ∠

s Thm.)

5. C

is the midpoint of AE⎯⎯⎯⎯⎯

(Given)

6. AC⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯

(Def. of mdpt.)

7. △ABC≅△EDC

(by ASA)

There you go

(from Lesson)

You might be interested in
18 lollipop at the same number of lollipops on the nine tables how many levels did she pop on each table​
vivado [14]

Answer:

2

Step-by-step explanation:

.....................

7 0
2 years ago
How can you find discount and markup
melamori03 [73]
By using different math operations
5 0
3 years ago
Consider the following data set:<br><br> 0, 10, 12, 3, 13, 7, 2, 5<br><br> Find the upper quartile.
weeeeeb [17]

Answer:

11

Step-by-step explanation:

The upper quartile Q3 is the median of the upper half of the data.

6 0
2 years ago
Work out the value of 4(2x+3y) when x=8 and y=-3
meriva
4(2 x 8 + 3 x (-3))
4(16 + (-9))
4(7)
=28

8 0
2 years ago
Edward has 18 apples and 16 oranges to share. He has 26 friends in his class. He wants to give each friend one fruit. How many f
jasenka [17]

Answer:

he' ll have 8 fruits left

Step-by-step explanation:

18 + 16  =  34 ,  34-26 = 8

5 0
1 year ago
Read 2 more answers
Other questions:
  • write two linear functions, f(x) and g(x). For example, f(x)= 3x-7 and g(x)= -2x+5. Then see whether f(x) - (-g(x)) is equivalen
    6·1 answer
  • I need help with this someone!!
    15·2 answers
  • When can 1/3 be bigger than 1/2
    14·2 answers
  • Look at Arnold's attempt to solve the equation for b:
    12·1 answer
  • Kevin bought 2 pairs of jeans that were originally $40 per pair but were each marked down by $15 and 3 t-shirts for $12 each. He
    15·1 answer
  • What is the volume of a sphere with a radius of 3 inches?
    11·2 answers
  • Ellie has b blue pencils and y yellow pencils. how many pencils doe she have in total
    13·1 answer
  • How to divide0.8 into 30
    12·2 answers
  • Plz help me plz help me​
    10·1 answer
  • Cookie or whatever you want.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!