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
Over [174]
3 years ago
7

In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets AC at point H and the angle bisector of ∠C meets AB at point K. Prove that BH

≅ CK.

Mathematics
1 answer:
solniwko [45]3 years ago
5 0

Answer:

See explanation

Step-by-step explanation:

In ΔABC, m∠B = m∠C.

BH is angle B bisector, then by definition of angle bisector

∠CBH ≅ ∠HBK

m∠CBH = m∠HBK = 1/2m∠B

CK is angle C bisector, then by definition of angle bisector

∠BCK ≅ ∠KCH

m∠BCK = m∠KCH = 1/2m∠C

Since m∠B = m∠C, then

m∠CBH = m∠HBK = 1/2m∠B = 1/2m∠C = m∠BCK = m∠KCH   (*)

Consider triangles CBH and BCK. In these triangles,

  • ∠CBH ≅ ∠BCK (from equality (*));
  • ∠HCB ≅ ∠KBC, because m∠B = m∠C;
  • BC ≅CB by reflexive property.

So, triangles CBH and BCK are congruent by ASA postulate.

Congruent triangles have congruent corresponding sides, hence

BH ≅ CK.

You might be interested in
(x + y + 2)(y + 1)<br> Solve
RideAnS [48]

Hello there! We are given the following equation and want to simplify it:

(x+y+2)(y+1)

First, let's use the Distributive Property:

  • (a+b)(c)=ac+bc

For this step, we are going to let:

  • a=y
  • b=1
  • c=(x+y+2)

After applying this version of the Distributive Property, we are given the equation:

(y)(x+y+2)+(1)(x+y+2)

We're going to use the distributive party again, but a slightly different version that's almost the same as first:

  • (a)(b+c+d)=ab+ac+ad

Using this on both terms of the equation changes the equation to:

(xy+y^2+2y)+(x+y+2)

Now, we just remove the parenthesis and combine like terms

y^2+3y+xy+x+2

This should be your answer. Let me know if you need any clarifications, thanks!

~ Padoru

6 0
2 years ago
The ratio of quarters to dimes in a coin collection is 5 : 3. You add the same number of new quarters as dimes to the collection
kondaur [170]

Answer:

Step 1. The answer is no.

Step 2. The answer is b.

Step-by-step explanation:

I think Step 2 already sort of explains the reasoning behind the answer for step 1.

Hope this helps!

3 0
3 years ago
Read 2 more answers
Amanda has 15 coins in her pocket. Of these, 8 are quarter. What is ratio of quarters to coins in Amanda's pocket?i
deff fn [24]
8:15 or 8 to 15 would be the ratio because you compare 8 quarters to 15 coins.
5 0
3 years ago
Read 2 more answers
If the suspect is found guilty, then he will go to prison.
Marrrta [24]

Answer:

If the suspect goes to prison, then he was found guilty.

Step-by-step explanation:

Means the same thing. If you guilty, you get the jail time. Same thing as before. The only other one it could be is the first one. But you could argue that one.

4 0
2 years ago
- A six-foot diameter circular table
IrinaVladis [17]

Answer:

28.26

Step-by-step explanation:

area of a circle is (pi)(r)^2

radius is half of the diameter

6/2=3

3 feet is the radius

a= 3.14 (3)^2

=3.14 x 9

= 28.26 feet

6 0
2 years ago
Read 2 more answers
Other questions:
  • Determine whether the given differential equation is exact. if it is exact, solve it. (if it is not exact, enter not.) (3x + 6y)
    11·1 answer
  • Does 23y+50+27y=50y+50 have one solution, no solution, or infinite solutions
    12·2 answers
  • What was her heart rate one half hour after beginning the workout
    6·1 answer
  • There are 42 pairs of shoes at the skate rental office.How many individual shoes are there in all?
    5·2 answers
  • What are two different ways for finding the area of the shaded region. All angles are right angles.
    10·2 answers
  • Find x when y=5 in the literal equation 4x+7y=51
    5·2 answers
  • If 15% of a number is 30 and 40% of the same number is 80, find 25% of that number.
    7·1 answer
  • 2,550 gallons in 30 days i wish if you plz explain it.
    12·2 answers
  • Please please please help me I’ll give brainly
    5·2 answers
  • A triangle has an angle that measures 95°. The other two angles are in a ratio of 6:11. What are the measures of those two angle
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!