[tex] \underline{ \underline{ \text{Question}}} : [/tex]
In the adjoining figure , ABC is an isosceles triangle. BO and CO are the bisectors of [tex] \angle[/tex] ABC and [tex] \angle[/tex] ACB respectively. Prove that BOC is an isosceles triangle.
~Thanks in advance !
![[tex] \underline{ \underline{ \text{Question}}} : [/tex]In The Adjoining Figure , ABC Is An Isosceles](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/9IR3XgX79oxTHAmOAL8xQtxS8ZMKdSbS.jpeg)
Answers
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 .Figure :-
[tex] \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$}\end{picture}[/tex]
If LaTeX doesn't work on app kindly see the attachment .
Here we will use a theorem which is ,
[tex]\large\underline{\underline{\textsf{\textbf{\red{\blue{$\leadsto$} Theorem :- }}}}}[/tex]
Sides opposite to equal angles are equal.Hence here,
[tex]\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} }[/tex]
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.
Hence Proved !![[tex] \underline{ \underline{ \text{Question}}} : [/tex]In The Adjoining Figure , ABC Is An Isosceles](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/NT2TEI3wINzzSNqlJFTL1hvxf64h9TmI.jpeg)
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:
[tex]\angle ABC=\angle ACB[/tex]
∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:
[tex]\angle ABO+\angle CBO =\angle ACO+\angle BCO[/tex]
Since ∠ABO =∠ACO, by substitution:
[tex]\angle ABO+\angle CBO =\angle ABO+\angle BCO[/tex]
Subtracting ∠ABO from both sides produces:
[tex]\angle CBO=\angle BCO[/tex]
So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.
Related Questions
If you could help I would really appreciate it, but if not that’s fine. Thank you.
Answers
3•(2) -5
6-5
1
The answer is 1!
3+2x=17 I’m taking a test
Answers
Answer: x=7
Step-by-step explanation:
2x=17-3
2x=14
X=7
-3 + 2x = 17 -3
2x = 14
2x/2 = 14/2
x = 7
2/3 + 9/12 add fractions with unlike denominators
Answers
Answer:
[tex]1\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} + \frac{9}{12}[/tex] <-- let's change 2/3 into a fraction that has 12 as the denominator
[tex]\frac{2}{3}[/tex] × 4 <-- multiply both the numerator and the denominator by 4
2 × 4 = 8 <-- new numerator
3 × 4 = 12 <-- new denominator
now we have [tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex]
[tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex] = [tex]\frac{17}{12}[/tex] <-- let's change it into a mixed number
17 ÷ 12 = [tex]1\frac{5}{12}[/tex]
Answer: its 17/12
Step-by-step explanation:
What is the image point of (-7,7) after a translation right 1 unit and down 3 units?
Answers
Answer:
Step-by-step explanation:
We start at (-7, 7). A translation of 1 unit to the right results in (-6, 7). A translation down from there results in (-6, 4). This is the desired image point.
A company rents out 10 food booths and 25 game booths at the county fair. The fee for a food booth is $100 plus $2 per day. The fee for a game booth is $50 plus $3 per day. The fair lasts for n days, and all the booths are rented for the entire time. Enter and simplify an expression for the amount in dollars that the company is paid.
Answers
Answer:
2,250 + 95n
Step-by-step explanation:
Cost of a food booth = 100 + 2n
Cost of 10 food booth = 10(100 + 2n)
= 1,000 + 20n
Cost of a game booth = 50 + 3n
Cost of 25 game booth = 25(50 + 3n)
= 1,250 + 75n
Total amount earned by the company = Cost of 10 food booth + Cost of 25 game booth
= (1,000 + 20n) + (1,250 + 75n)
= 1,000 + 20n + 1,250 + 75n
= 1,000 + 1,250 + 20n + 75n
= 2,250 + 95n
Total amount earned by the company = 2,250 + 95n
What is the greatest common factor of 3 and 6? O3 O 6 O 18 O 36
Answers
Answer:
3 I believe
Step-by-step explanation:
The factors of 3 are: 1, 3
The factors of 6 are: 1, 2, 3, 6
Then the greatest common factor is 3.
Answer:
3 is the great common factor
Step-by-step explanation:
factors:
3- 1,3
6- 1,2,3,6
hope it helps:))
Write the polynomial in standard form. Then find its degree and the leading coefficient.
2 + 4c - 303 + 6c5
The polynomial in standard form is? __
Answers
Answer:
6c^5+4c−301, assuming that you meant 6c^5
The sum of two numbers is 30 and their difference is 12, what are the two numbers
Answers
Answer:
Sum: 21 + 9 = 30
Difference: 21 - 9 = 12
Step-by-step explanation:
Let the number is a and b
The sum of two numbers =30
so,a+b=30 ............(1)
The difference of two number =12
so,a-b=12 .................(2)
If we add two equation (1) and (2)
we get,
a+b+a-b=30+12
2a=42
[tex]\tt{ a=\dfrac{42}{2} }[/tex]
[tex]\tt{ a=21 }[/tex]
so,one number is a=21
if we put the value a in (2) equation
we get,
a-b=12
21-b=12
b=21-12
b=9
so,the another number is=b=9
[tex]\tt{ the~two~ number~ are~ 21 ~and~ 9 }[/tex]
Find the slope (m) of the line
that passes through the pair of
points
(4.5, 5.7) and (14.5, 18.9)
Answers
Solve the equation using subtraction,
3x-4y=-7
3x+y=13
Answers
Answer:
Step-by-step explanation:
first question is -1
and i think the sec option is 13/3+y/3 i think im wrong on the sec option
Simplify (6⁴)³
A. b
B. b³
C. b⁹
D. b¹²
Answers
it would be b^12
Hope this helps <3
3x - 4y = 44
can someone help me get Y by it self
Answers
Answer:
y= 3 /4 x−11
Step-by-step explanation:
3x - 4y = 44
Add -3x to both sides.
3x−4y+−3x=44+−3x
−4y=−3x+44
Divide both sides by -4.
−4y /−4 = (−3x+44 )/−4
y= 3 /4 x−11
PLEASD HELP!!! I have no clue how to do this
Answers
Step-by-step explanation:
[tex]for1 \\ x =8 \\ y = x \sqrt{2} = 8 \sqrt{2 } = 11.31[/tex]
[tex]for2 \\ x =25 \sqrt{2} = 35.36 \\ y = 25[/tex]
[tex]for3 \\ 19 = x \sqrt{2} \\ x = \frac{19}{ \sqrt{2} } = 13.44 \\ y = 13.44 \\ [/tex]
Find the slope of the line
Answers
Answer:
-2
Step-by-step explanation:
Rise 2
___ ___
Run -1
which equals -2
pls help me answer this :’)
Answers
Answer:
Commutative and multiplicative identity
Step-by-step explanation:
mark brainlyist
Which of the following represents the lowest speed in miles per hour?
6 miles in 1/8 hour
11 miles in 1/4 hour
16 miles in 3/8 hour
20 miles in 1/2 hour
Answers
Answer:
C . 16 miles in 3/6 hour. Because 3/6 is 1/2. So, the answer would basically be 16 miles in 1/2.
pls help me asap-
what is the length of segment FE?
Answers
Answer:
FE=√210=14.49.
Step-by-step explanation:
In right triangle EFH,angle EFH is 90°and FG is perpendicular to EH.
Therefore,
FE²= EG.EH
FE²=10×(10+11)
=10×21
FE²=210
FE= √210
Pls help !!! Thank you
Answers
Answer:
y-10=2/3(x-8)
Step-by-step explanation:
(y2-y1)/(x2-x1) is the equation for slope so put your points in you get 2/3 once simplified then its just a matter of putting points in the equation y-y1= m(x-x1)
Mary plants roses in 14 of her garden. She also plants some tulips in her garden. She has 112 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
Answers
Answer:
112/126 = 8/9
Step-by-step explanation:
Answer:
Step-by-step explanation:
yur gay
approximate the length of the hypotenuse to the nearest tenth without adding a calculator
Answers
Answer:
hypotenuse=6.4
Step-by-step explanation:
One side is 4 units and the other is 5 units.
Hypotenuse= c^2
a^2+b^2=c^2
5^2+4^2=c^2
25+16=c^2
41=c^2
√41=c
c=6.4
Simplify:
√27x^2y^2
A) 27xy
B) 3xy
C) 3xy√3
D) xy√27
Answers
Answer:
[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]
Hence, option C is correct.
Step-by-step explanation:
Given the expression
[tex]\sqrt{27x^2y^2}[/tex]
simplifying the expression
[tex]\sqrt{27x^2y^2}=\sqrt{27}\sqrt{x^2}\sqrt{y^2}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=\sqrt{27}x\sqrt{y^2}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=\sqrt{27}xy[/tex]
[tex]=xy\sqrt{3^3}[/tex]
[tex]=xy\sqrt{3^2\cdot \:\:3}[/tex]
Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=3xy\:\sqrt{3}[/tex]
Therefore,
[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]
Hence, option C is correct.
Given: AACD is isosceles with angle D as the vertex angle. B is the midpoint of AC. AB= x + 5, BC= 2x - 3, and CD = 2x + 6. Find the perimeter of ∆ACD.
Answers
Answer:
70 unitsStep-by-step explanation:
Given triangle ACD
AB = BCCD = 2x + 6AB = x + 5BC = 2x - 3P = ?Perimeter is sum of the side lengths:
P = AD + CD + ACAD = CD because D is vertex and the triangle is isosceles
AC = AB + BC because B is midpoint of AC
Then P is:
P = 2(2x + 6) + (x + 5) + (2x -3) = 4x + 12 + x + 5 + 2x - 3 = 7x + 14Find the value of x from the AB = BC:
x + 5 = 2x - 32x - x = 5 + 3x = 8Then find the value of P:
P = 7*8 + 14 = 56 + 14 = 70 units8
3. Explain the steps to solve
X+3
X+6
Answers
Answer:
x=6,-4
Step-by-step explanation:
solve for x by cross multiplying
Please ANSWER THE ANSWER HAS TO BE A INTEGER OR A DECIMAL.
Answers
Answer: 4.3
Step-by-step explanation: To find the range you have to subtract the highest number by the lowest number. So you'd subtract 2.6 by -1.7. And since -1.7 is already a negative number, it would get turned into a positive.
Solve for x: x - 2 > 2x + 12.
Ox> 14
0x< 14
Ox>-14
Ox<-14
Answers
Answer:
Solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]
Option D is correct option.
Step-by-step explanation:
We need to solve the inequality: [tex]x - 2 > 2x + 12[/tex] and find value of x
Solving the inequality
[tex]x - 2 > 2x + 12[/tex]
First of all, we will add 2 on both sides
[tex]x - 2+2 > 2x +12 +2\\x>2x+14[/tex]
Now, add -2x on both sides of inequality
[tex]x-2x>2x+14-2x\\-x>14[/tex]
Now, multiply both sides by -1, when multiplying by negative number, the inequality is reversed i.e. > will become <
[tex]-1*-x<14*-1\\x<-14[/tex]
So, solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]
Option D is correct option.
For the problem below, find the percent of change. Then decide whether is it a percent increase or a percent decrease. Round to the nearest whole
percent if necessary.
100 acres to 140 acres:
Answers
Answer:
cx
Step-by-step explanation:
g
Question 6 of 10
Two triangles that have the same side lengths will always be congruent.
A. True
B. False
Answers
Answer:
True.
Step-by-step explanation:
We have to tell about the statement true or false
Two triangles that have the same side length will always be congruent
The SSS congruency rule states that if all three sides of one triangle are equal to corresponding three sides of another triangle, then the triangles are congruent.
∴ we say that when the sides are the same then the triangles are congruent.
Hence, the statement is true.
Because the definition of a congruent triangle is a triangle with every side of same length.
A rectangular garden has a length of 2x - 7 and a width of 3x. Write a simplified expression to represent the area of the garden. (Hint: A=LW where, L is the Lenght and W is the Width). Simplify
Answers
Answer:
The answer is 6x² - 21x.
Step-by-step explanation:
You have to substitute the expressions inro the formula :
[tex]A = length \times width[/tex]
[tex]let \: l = 2x - 7,w = 3x[/tex]
[tex]A = (2x - 7) \times 3x[/tex]
[tex]A = 3x(2x - 7)[/tex]
[tex]A = 6 {x}^{2} - 21x[/tex]
The area of the rectangular garden is 6x² - 21x.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a rectangle is (length×width).
Given, The rectangular garden has a length of (2x - 7) and a width of 3x.
Therefore, The area of the garden is,
= (2x - 7)×3x.
= 6x² - 21x.
= x(6x - 21).
learn more about rectangles here :
https://brainly.com/question/28993977
#SPJ2
Use the diagram to the right to complete the statement. If m
m
Answers
Mhanifa please answer this question about lines