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
dem82 [27]
3 years ago
9

title=" \underline{ \underline{ \text{Question}}} : " alt=" \underline{ \underline{ \text{Question}}} : " align="absmiddle" class="latex-formula">
In the adjoining figure , ABC is an isosceles triangle. BO and CO are the bisectors of \angle ABC and \angle ACB respectively. Prove that BOC is an isosceles triangle.

~Thanks in advance !

Mathematics
2 answers:
Marina CMI [18]3 years ago
8 0
<h3><u>GiveN</u><u> </u><u>:</u><u>-</u></h3>
  • In the given figure , ABC is an isosceles triangle.
  • BO and CO are the bisectors of \angle ABC and \angle ACB respectively.

<h3><u>To</u><u> </u><u>ProvE</u><u> </u><u>:</u><u>-</u></h3>

  • ∆ BOC is isosceles.

<h3><u>ProoF</u><u> </u><u>:</u><u>-</u></h3>

Here it's given that ∆ABC is a isosceles triangle. We know that in a isosceles triangle opposite angles are equal. And the angles opposite to equal sides are also equal.

Hence here ,

  • AB = AC
  • ∠ ABC = ∠ACB .

<u>Figure</u><u> </u><u>:</u><u>-</u>

\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\put(0,0){\line(1,0){4}}\put(4,0){\line(-1,2){2}}\put(0,0.001){\line(1,2){2}}\put(0,0.01){\line(1,1){2}}\put(3.99,0){\line(-1,1){2}}\put(0,-0.3){$\bf B $}\put(4,-0.3){$\bf C$}\put(2,4.2){$\bf A$}\put(1.8,2.2){$\bf o$}\end{picture}

If LaTeX doesn't work on app kindly see the attachment .

Here we will use a theorem which is ,

\large\underline{\underline{\textsf{\textbf{\red{\blue{$\leadsto$} Theorem :- }}}}}

  • Sides opposite to equal angles are equal.

Hence here,

\tt:\implies \angle ABC =\angle ACB \\\\\tt:\implies \dfrac{1}{2}\times \angle ABC =  \dfrac{1}{2}\times \angle ACB \\\\\tt:\implies \boxed{\bf \blue{\angle OBC = \angle OCB} }

Now in ∆OBC , we can see that ∠OBC = ∠OCB. (just proved ) . Hence we can say that sides OB and OC are equal. Since the sides opposite to equal angles are equal. Therefore in ∆OBC , two sides are equal.

Therefore ∆ OBC is an isosceles triangle.

<h3><u>Hence </u><u>Proved</u><u> </u><u>!</u><u> </u></h3>

Lubov Fominskaja [6]3 years ago
7 0

Answer:

See Below.

Step-by-step explanation:

We are given the isosceles triangle ΔABC. By the definition of isosceles triangles, this means that ∠ABC = ∠ACB.

Segments BO and CO bisects ∠ABC and ∠ACB.

And we want to prove that ΔBOC is an isosceles triangle.

Since BO and CO are the angle bisectors of ∠ABC and ∠ACB, respectively, it means that ∠ABO = ∠CBO and ∠ACO = ∠BCO.

And since ∠ABC = ∠ACB, this implies that:

∠ABO = ∠CBO =∠ACO = ∠BCO.

This is shown in the figure as each angle having only one tick mark, meaning that they are congruent.

So, we know that:

\angle ABC=\angle ACB

∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:

\angle ABO+\angle CBO =\angle ACO+\angle BCO

Since ∠ABO =∠ACO, by substitution:

\angle ABO+\angle CBO =\angle ABO+\angle BCO

Subtracting ∠ABO from both sides produces:

\angle CBO=\angle BCO

So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.

You might be interested in
What is the ratio for tan (C)? (Hint: SOHCAHTOA)
Sever21 [200]

Answer:

D. 3/4

Step-by-step explanation:

tan(C) = opposite / adjacent = 3/4

4 0
3 years ago
Please can someone help. ill give brainliest
vodka [1.7K]

Step-by-step explanation:

upper left angle and lower right are the same in a parallelogram (the other two angles match as well, but aren't useful)

so we can write this equation:

3x -15 = 2x +24

1x -15 = 24

x = 39

always do the same thing on both sides of an equation (here: subtract 2x, then add 15)

now you might give it a try yourself with the next problem that got two same things in it.

always grow stronger :)

6 0
2 years ago
What is the solution of equations graphed below?<br>A. (2,4)<br>B. (4,2)<br>C. (0,6)<br>D. (6,0)​
vivado [14]

Answer:

(4,2)

Step-by-step explanation:

The solution to the system is where the two graphs overlap

The two graphs cross at x=4 y =2

(4,2)

3 0
2 years ago
Read 2 more answers
Two ratios that are equivalent to 2 : 9
NeTakaya

Answer:

4 : 18, 8 : 36

Step-by-step explanation:

We multiply to find equal ratios.

2 x 2 = 4

9 x 2 = 18

4 x 2 = 8

18 x 2 = 36

We get 4 : 18, 8 : 36.

7 0
2 years ago
Read 2 more answers
How many 1x1 unit cubes would equal the volume of the figure shown?
motikmotik
D 3500 kk bye now ! :))
3 0
2 years ago
Other questions:
  • Lola measures three buttons for a shirt she is making. one button is 1/8 inch, one is 3/8 inch, and one is 1/4 inch. the button
    7·1 answer
  • Solve the following dividend problem
    8·1 answer
  • Find 3 different possibile pairs of values for a and b ​
    15·2 answers
  • What is the variable in the expression 2/3 + u
    12·2 answers
  • Doreen lives 3/4 mile from the library Sheila lives 1/3 as far away from the library as Doreen. which one lives far from the lib
    5·1 answer
  • PLEASE HELP<br> 1/4 is to 1 1/4 as 2 is to b
    8·1 answer
  • 4(3r+2)-7x i need help every answer i get is wrong.
    12·2 answers
  • What is 0.0006009 written in scientific notation
    12·1 answer
  • Explain why the equations X - 13 = 4 and 13 - X = 4 do NOT have the same solution.
    12·1 answer
  • Please help me I need to find the slope intercept equation to go with the points ​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!