Chapter 4.1, Problem 24WE

To determine

To find: the number of triangles are there with one vertex at $P$ , another vertex on $I$ , and each triangle congruent to the given triangle.

Answer to Problem 24WE

There are six triangles congruent to given triangle with one vertex at $P$ and another vertex on line $l$ .

Explanation of Solution

Given information:

A scalene triangle and a point $P$ in same line $l$ .

Calculation:

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 $\Delta ABC$ and a line $l$ away $\Delta ABC$ with point $P$ on it.

Now, to draw triangles congruent to given $\Delta ABC$ with one vertex at $P$ and another vertex on line $l$ .

Firstly, consider that vertex $A$ of $\Delta ABC$ 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 $B$ on line $l$ .

Similarly, draw 4 more congruent triangles by considering vertex $B$ and vertex $C$ coincides with point $P$ on line $l$ and another vertex on line $l$ .

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