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liq [111]
3 years ago
7

Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

Mathematics
2 answers:
weeeeeb [17]3 years ago
7 0

<em>AC bisects ∠BAD, => ∠BAC=∠CAD ..... (1)</em>

<em>thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given), </em>

<em>                                       ∠BAC=∠CAD      [from (1)],</em>

<em>AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC</em>

<em>Hence,      by AAS axiom, ΔABC ≅ ΔADC,</em>

<em>Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)</em>

<em />

Hence, BC=DC proved.

olga55 [171]3 years ago
7 0

Answer:

Solution given;

<BCA=<ACD

<ABC=<ADC

now

In traingle ABC & ∆ ACD

AC=AC[common base]

<BCA=<ACD[bisector bisect it]

<ABC=<ADC[Given]

∆ABC is congruent to ∆ ACD by S.A.A. axiom

AB is congruent to AD.

[ corresponding sides of a congruent triangle are equal]

Hence proved.

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Fantom [35]

Answer:

The first option: -5/4x + 1/6.

Step-by-step explanation:

(3/4x - 2/3) - (-5/6 + 2x)

= (3/4x - 2/3) + 5/6 - 2x

= 3/4x - 2x - 2/3 + 5/6

= 3/4x - 8/4x - 4/6 + 5/6

= -5/4x + 1/6

So, the first option: -5/4x + 1/6.

Hope this helps!

6 0
3 years ago
At Polynomials Pizza, a large cheese pizza costs $6.50. Each additional topping for the pizza costs $1.45. The total for a large
dangina [55]

Answer:x

=

5

toppings

Step-by-step explanation:Total cost of cheese pizza:  

$

10.75

Any additional topping adds:  

+

$

1.25

So a cheese pizza with  

1

additional topping is:

$

10.75

+

$

1.25

=

$

12.00

A cheese pizza with  

2

additional toppings is:

$

10.75

+

$

1.25

+

$

1.25

=

$

10.75

+

2

×

$

1.25

=

$

13.25

A cheese pizza with  

3

additional toppings is:

$

10.75

+

$

1.25

+

$

1.25

+

$

1.25

$

10.75

+

3

×

$

1.25

=

$

14.50

If you pay attention to the pattern you can see that, for any number of toppings, say  

x

toppings, the price is going to be:

$

10.25

+

x

×

$

1.25

We are told the final cost is  

$

17.00

. That is

$

10.25

+

x

×

$

1.25

=

$

17.00

Subtract  

$

10.25

from both sides

$

10.25

−

$

10.25

+

x

×

$

1.25

=

$

17.00

−

$

10.25

x

×

$

1.25

=

$

6.25

Divide both sides by  

$

1.25

x

×

$

1.25

$

1.25

=

$

6.25

$

1.25

x

=

5

4 0
3 years ago
Read 2 more answers
How do you evaluate 3f(2)
d1i1m1o1n [39]

The answer should be 6f. You multiply the 3 and the 2 and then put the f at the end (:

5 0
3 years ago
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A gumball machine has 220 red gumballs. If the red gumballs are 50% of the total number of gumballs, how many gumballs are in
JulijaS [17]
Answer:

440

Explanation:

If 50% of the total gum balls are red which is 220, then the other 50% is 220.
5 0
3 years ago
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Zinaida [17]
You can express the edge lengths in terms of "cubes" or you divide the total volume by the volume of a cube. It works either way.

Edge lengths are
.. 80 cubes by 8 cutes by 13 cubes
so total volume is
.. (80 * 8 * 13) = 8320 cubes


In cubic inches, the volume is
.. (20 in)*(2 in)*(3 1/4 in) = 130 in^3.
The volume of a 1/4-in cube is (1/4 in)^3 = 1/64 in^3.
Then the number of cubes that will fit in the prism is
.. (130 in^3)/(1/64 in^3) = 8320 . . . . cubes

8320 cubes are needed to fill the rectangular prism.
7 0
3 years ago
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