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arlik [135]
3 years ago
12

Which statement is an example of the transitive property of congruence?

Mathematics
2 answers:
Westkost [7]3 years ago
5 0
An example of the transitive property of congruence is <span>D. If and , then .</span>
AlexFokin [52]3 years ago
4 0

Answer:

D. If  and , then is an example of transitive property of congruence.

Step-by-step explanation:

Transitive property of congruenc: If one segment is congruent to second segment and second is congruent to third segment then the segment one is congruent to third segment.

For example: If \overline{ AB} \cong  \overline {BC}

and \overline{BC} \cong \overline{CD}

Then \overline{AB} \cong  \overline {CD}

Therefore we can see in angles

If \angle ABC \cong \angle BCA

And \angle BCA \cong \angle CAB

Then \angle ABC\cong \angle CAB

Therefore, the statement of transitive property written as

If and, then

Hence, If and,  then is an example of the transitive property of congruence.

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A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of te triangle is 16m to the power of 2, what are the base
Olenka [21]

Answer:

The base of triangle is  \frac{8}{\sqrt{3}} \ m and the height of triangle is  \frac{12}{\sqrt{3}} \ m.

Step-by-step explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle = x\times\frac{1}{2} =\frac{x}{2} \ m.

The height of triangle = x\times \frac{3}{4} =\frac{3x}{4}\ m.

The area of triangle = 16\ m^2.

Now, we put the formula of area to solve:

Area=\frac{1}{2} \times base\times height

16=\frac{1}{2} \times \frac{x}{2} \times \frac{3x}{4}

16=\frac{3x^2}{16}

<em>Multiplying both sides by 16 we get:</em>

<em />256=3x^2<em />

<em>Dividing both sides by 3 we get:</em>

<em />\frac{256}{3} =x^2<em />

<em>Using square root on both sides we get:</em>

\frac{16}{\sqrt{3}}=x

x=\frac{16}{\sqrt{3}}

Now, by substituting the value of x to get the base and height:

Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.

<em>So, the base of triangle = </em>\frac{8}{\sqrt{3}} \ m.<em />

Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.

<em>Thus, the height of triangle =  </em>\frac{12}{\sqrt{3}} \ m.<em />

Therefore, the base of triangle is  \frac{8}{\sqrt{3}} \ m and the height of triangle is  \frac{12}{\sqrt{3}} \ m.

7 0
3 years ago
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