Question

1. given the diagram below, classify each triangle by sides and angles. circle one selection from each column for each triangle

classify △abc by angles and sides
angles (circle one) sides (circle one)
acute scalene
right isosceles
obtuse equilateral

classify △dec by angles and sides
angles (circle one) sides (circle one)
acute scalene
right isosceles
obtuse equilateral

Explanation:

Step1: Find angles of $\triangle ABC$

In $\triangle ABC$, $\angle B = 50^{\circ}$, $\angle ACB=180 - 50 - 70=60^{\circ}$ (linear - pair with $\angle DCE = 50^{\circ}$ and angle - sum property of a triangle), $\angle A=180-(50 + 60)=70^{\circ}$. All angles are less than $90^{\circ}$, so it is acute.

Step2: Analyze sides of $\triangle ABC$

Since all angles are different, all sides are different. So it is scalene.

Step3: Find angles of $\triangle DEC$

$\angle D = 70^{\circ}$, $\angle C = 50^{\circ}$, $\angle E = 60^{\circ}$. All angles are less than $90^{\circ}$, so it is acute.

Step4: Analyze sides of $\triangle DEC$

Since all angles are different, all sides are different. So it is scalene.

Answer:

Classify $\triangle ABC$:

• Angles: Acute
• Sides: Scalene

Classify $\triangle DEC$:

• Angles: Acute
• Sides: Scalene