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
Tamiku [17]
2 years ago
11

Heya! ツ

Mathematics
2 answers:
fiasKO [112]2 years ago
5 0

Answer:

See Below.

Step-by-step explanation:

In the given figure, O is the center of the circle. Two equal chords AB and CD intersect each other at E.

We want to prove that I) AE = CE and II) BE = DE

First, we will construct two triangles by constructing segments AD and CB. This is shown in Figure 1.

Recall that congruent chords have congruent arcs. Since chords AB ≅ CD, their respective arcs are also congruent:

\stackrel{\frown}{AB }\, \cong\, \stackrel{\frown}{CD}

Arc AB is the sum of Arcs AD and DB:

\stackrel{\frown}{AB}=\stackrel{\frown}{AD}+\stackrel{\frown}{DB}

Likewise, Arc CD is the sum of Arcs CB and DB. So:

\stackrel{\frown}{CD}=\stackrel{\frown}{CB}+\stackrel{\frown}{DB}

Since Arc AB ≅ Arc CD:

\stackrel{\frown}{AD}+\stackrel{\frown}{DB}=\stackrel{\frown}{CB}+\stackrel{\frown}{DB}

Solve:

\stackrel{\frown}{AD}\, \cong\,\stackrel{\frown}{CB}

The converse tells us that congruent arcs have congruent chords. Thus:

AD\cong CB

Note that both ∠ADC and ∠CBA intercept the same arc Arc AC. Therefore:

\angle ADC\cong \angle CBA

Additionally:

\angle AED\cong \angle CEB

Since they are vertical angles.

Thus:

\Delta AED\cong \Delta CEB

By AAS.

Then by CPCTC:

AE\cong CE\text{ and } BE\cong DE

stepladder [879]2 years ago
3 0

Answer:

this is your answer. look it once.

You might be interested in
-18 > |-1 (3-2x)| > 18
12345 [234]

Answer:

No Solution

Step-by-step explanation:

Since -18 > 18 is not true, this inequality is always false

4 0
3 years ago
Read 2 more answers
There are about 16 kilometers in 10 miles. About how many kilometers are in 5 miles
SSSSS [86.1K]

Answer:

8.04672

or 8

Step-by-step explanation:

4 0
2 years ago
A store has apples on sale for $3.00 for 2 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $18.00
Temka [501]

Answer:

19

Step-by-step explanation:

3 0
3 years ago
If Sandra practices the piano each day for 2/3 of an hour, how many hours of practice will she get in each week?
dimulka [17.4K]

Answer:

4 2/3

Step-by-step explanation:

2/3 * 7/1

4 2/3

8 0
3 years ago
Find the measure of the largest angle in the triangle shown . PLS HELP
Andre45 [30]

Answer:

72°

Step-by-step explanation:

So the three angles of a triangle always add up to 180°. This means that

15x + 21x + 24x = 180

This becomes:

60x = 180

And solves as:

x = 3

The largest angle has to be the one marked with 24x because it has the largest coefficient and x is a constant.

24x = 24(3) = 72

The measure of the largest angle in the triangle is 72°.

4 0
2 years ago
Read 2 more answers
Other questions:
  • Is 1,1 2,2 3,5 4,10 5,15 a function
    9·1 answer
  • Solve 250 ÷ 5 ÷ 10 making sure to divide in the proper order.
    6·2 answers
  • ∠A and ∠B are vertical angles. If ∠A=8x+14 and ∠B=2x+50, what is m∠B?
    7·1 answer
  • HELP ASAP! PLS!! The Water Department checks the city water supply on a regular basis for
    9·2 answers
  • A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 1
    14·1 answer
  • Which expression is equivalent to 5^0?
    15·1 answer
  • Is the equation y = x ^2 + 3 a function?
    6·2 answers
  • If x + y = x y = 5 then x ^2 y + X Y ^ 2 equals​
    15·1 answer
  • 5) A student is given a metal sphere about the size of a softball and asked to identify what type of
    8·1 answer
  • What are the first five terms of the sequence an= n +8?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!