Question

in exercises 3 - 6, classify the triangle by its sides and by measuring its angles. (see example 1.)
3.
4.

Explanation:

Step1: Classify by sides

• For triangle \(XYZ\):
• Two sides (\(XY\) and \(YZ\)) are marked as equal. So, it is an isosceles triangle (a triangle with at least two equal - sided).
• For triangle \(LMN\):
• All three sides are marked as equal. So, it is an equilateral triangle (a triangle with all three sides equal).

Step2: Classify by angles

• For triangle \(XYZ\):
• There is a right - angle (\(90^{\circ}\)). So, it is a right - angled triangle.
• For triangle \(LMN\):
• All angles in an equilateral triangle are \(60^{\circ}\) (since the sum of angles in a triangle is \(180^{\circ}\) and all angles are equal in an equilateral triangle). So, it is an acute - angled triangle (a triangle with all angles less than \(90^{\circ}\)).

Answer:

• For triangle \(XYZ\):
• By sides: Isosceles triangle.
• By angles: Right - angled triangle.
• For triangle \(LMN\):
• By sides: Equilateral triangle.
• By angles: Acute - angled triangle.