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Ratling [72]
3 years ago
8

Explain why ΔADB ≅ ΔCDB. List the other corresponding parts.

Mathematics
1 answer:
anygoal [31]3 years ago
3 0

Answer:

Therefore the Correct option is First one

SAS, ∠A ≅ ∠C,  AB ≅ CB , ∠ABD ≅ ∠CBD .

Step-by-step explanation:

Given:

∠BDA ≅ ∠BDC

AD ≅ CD

TO Prove

ΔADB ≅ ΔCDB

Proof:

In  ΔADB  and ΔCDB  

AD ≅ CD               ....……….{Given}

∠BDA ≅ ∠BDC     …………..{Given}

BD ≅ BD               ....……….{Reflexive Property}

ΔADB ≅ ΔCDB  ….{By Side-Angle-Side Congruence Postulate}

∴ ∠A ≅ ∠C  ......{Corresponding Parts of Congruent Triangle are Congruent}

  AB ≅ CB  ......{Corresponding Parts of Congruent Triangle are Congruent}

∠ABD ≅ ∠CBD {Corresponding Parts of Congruent Triangle are Congruent}

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Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
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The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
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x + y/2 + z =30
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So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

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Answer:

Step-by-step explanation:

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Answer:

The lengths of all sides of the triangle will be 21 cm, 21 cm, and 21 cm

Step-by-step explanation:

Given that the perimeter of the triangle = 63 cm

And the length of one side = 21 cm

and one of the medians is perpendicular to one of its angle bisectors

Since triangle has 3 sides,

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3 0
3 years ago
Suppose that in a random selection of 100 colored​ candies, 28​% of them are blue. The candy company claims that the percentage
Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29​%.

Step-by-step explanation:

We are given that in a random selection of 100 colored​ candies, 28​% of them are blue. The candy company claims that the percentage of blue candies is equal to 29​%.

Let p = <u><em>population percentage of blue candies</em></u>

So, Null Hypothesis, H_0 : p = 29%     {means that the percentage of blue candies is equal to 29​%}

Alternate Hypothesis, H_A : p \neq 29%     {means that the percentage of blue candies is different from 29​%}

The test statistics that will be used here is <u>One-sample z-test for</u> <u>proportions</u>;

                         T.S.  =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of blue coloured candies = 28%

           n = sample of colored​ candies = 100

So, <u><em>the test statistics</em></u> =  \frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }

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The value of the z-test statistics is -0.22.

<u>Also, the P-value of the test statistics is given by;</u>

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Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, <u><em>so we insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29​%.

4 0
3 years ago
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