A quadrilateral is a shape with four sides . in the quadrilateral GRIT below , two triangles are formed by constructing GI. Prove that both triangles are right triangles .

Answer 1

To prove that both triangles formed by constructing GI in the quadrilateral GRIT are right triangles, let's name the points as follows:

G - Quadrilateral vertex
R - Quadrilateral vertex
I - Point of intersection of GR and TI
T - Quadrilateral vertex

We are going to prove that both triangles GIT and GIR are right triangles by proving that one of their angles is equal to 90 degrees.

1. Triangle GIT:
The line GR is a straight line passing through the quadrilateral vertices G and R. The line TI is perpendicular to GR since it intersects it at point I. Therefore, the angle GIT is a right angle of 90 degrees.

2. Triangle GIR:
Similarly, the line GT is a straight line passing through the quadrilateral vertices G and T. The line RI is perpendicular to GT since it intersects it at point I. Therefore, the angle GIR is a right angle of 90 degrees.

In both triangles GIT and GIR, one angle is 90 degrees, which means that both triangles are right triangles.