Question

1. in the diagram below, segment rs and rt intersect line de at points t and s.

which of these statements is true about triangle rst?

options:

• triangle rst is an isosceles triangle.
• triangle rst is a scalene triangle.
• triangle rst is an equilateral triangle.
• triangle rst is a right triangle.

Explanation:

Step1: Find angles at T and S

Adjacent angles on a straight line sum to \(180^\circ\). So, \(\angle RTS = 180^\circ - 130^\circ = 50^\circ\), \(\angle RST = 180^\circ - 130^\circ = 50^\circ\).

Step2: Analyze triangle type

In \(\triangle RST\), \(\angle RTS=\angle RST = 50^\circ\). By the definition of isosceles triangle (two equal angles), \(\triangle RST\) is isosceles. Scalene (all angles different), equilateral (all \(60^\circ\)), and right (one \(90^\circ\)) don't apply here.

Answer:

Triangle RST is an isosceles triangle.