Rectangle Rest Find angle 𝒙. Show that ΔBDE is isosceles. 1. The diagram shows a rectangle that just touches one side of an equilateral triangle. Find angle 𝒙. Show your working and reasoning. 2. The rectangle now rests on the apex of the triangle, making ABC a straight line. Show that ΔBDE is isosceles.

Rectangle Rest Find angle 𝒙. 1. The diagram shows a rectangle that just touches one side of an equilateral triangle. Find angle 𝒙. Show your working and reasoning. Angles in an equilateral triangle are all 60° and angles on a line add up to 180°. Therefore the other base angle of the enclosed triangle is 120°. Angles in a triangle add up to 180°. Therefore the top angle of this triangle is 40°. Angles on a line add up to 180° and angles in a rectangle are 90°. Therefore 𝑥 must be 180−40−90. 𝒙=𝟓𝟎°

Rectangle Rest Show that ΔBDE is isosceles. 2. The rectangle now rests on the apex of the triangle, making ABC a straight line. Show that ΔBDE is isosceles. Angles in an equilateral triangle are all 60°, angles in a rectangle are all 90° and angles on a line add up to 180°. Therefore angle 𝐷 𝐵 𝐸 is 180−60−90=30°. Angles in an equilateral triangle are all 60° and angles on a line add up to 180°. Therefore angle 𝐷 𝐸 𝐵 is 180−60=120°. Angles in a triangle add up to 180°. Therefore angle 𝐵 𝐷 𝐸 is 180−30−120=30°. Since 𝐷 𝐵 𝐸=𝐵 𝐷 𝐸, triangle 𝑩𝑫𝑬 is isosceles.