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Suppose you are given a scalene triangle and a point Pon some line l. How many triangles are there with one vertex at P, another vertex onl, and each triangle congruent to the given triangle.

Short Answer

Expert verified

There are six triangles congruent to given triangle with one vertex atP and another vertex on linel.

Step by step solution

01

Step 1. Define a Scalene triangle.

A triangles in which all three sides are unequal is called a scalene triangle.

02

Step 2. State the explanation.

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then say that the corresponding angles and the sides of the triangles are congruent.

Draw a scalene ABCand a linelaway ABCwith point Pon it.

Now, to draw triangles congruent to given ABCwith one vertex at P and another vertex on line localid="1638428206263" l.

Firstly, consider that vertex Aof ABC coincides with point P on line l and another vertex C lie on line l and draw figure accordingly.

In a similar way, draw one more congruent triangle by taking vertex Bon line l.

Similarly, draw 4 more congruent triangles by considering vertex Band vertex Ccoincides with point Pon line land another vertex on line l.

Thus, there are six triangles congruent to given triangle with one vertex at Pand another vertex on line l.

03

Step 3. State the conclusion.

Therefore, there are six triangles congruent to given triangle with one vertex at Pand another vertex on line l.

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