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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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If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3
horrorfan [7]

Answer:  The correct option is (B) 24 : 25.

Step-by-step explanation:  Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Therefore, the ratio of the area of R to the area of S is

\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.

Thus, the required ratio of the area of R to the area of S is 24 : 25.

Option (B) is CORRECT.

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