18.7k views
5 votes
Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.

Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.-example-1

1 Answer

6 votes

a.

Using the compass, first let's find the point T'.

We put one part of of the compass in point S, then we adjust the other part to be on point T, finally we draw an arc, crossing the line m and the dashed line perpendicular to m that passes through T.

The intersection of this arc and the dashed line will be point T':

Doing the same procedure for point R, we find point R':

Finally, since point S is on line m, the point S' will be coincident to point S.

Drawing the triangle R'S'T', we have:

b.

They are coincident because the point is on the reflection line.

c.

Drawing segment TT', we have:

Since the distance from T to line m and T' to line m are the same and the intersection point is a right angle, we have two smaller congruent triangles, so the triangle STT' is isosceles.

Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.-example-1
Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.-example-2
Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.-example-3
Obtuse triangle ∆RST is shown below along with line m. Point S lines on m.-example-4
User Wildmonkey
by
6.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.