Let's analyze the triangle shown in the image:
Given:
- One angle is
90° (indicated by the right angle symbol).
- Two angles are
45° each.
- Side lengths: one leg is
4.8, the other leg is also
4.8, and the hypotenuse is
6.8.
---
Step 1: Check the angles
We know that:
- The sum of angles in a triangle is 180°.
- We have: 90° + 45° + 45° = 180° →
✔
So, this is a
right triangle because it has a 90° angle.
Also, since two angles are equal (45°), the sides opposite them must be equal. Indeed, both legs are labeled
4.8, so the triangle has
two equal sides.
This makes it an
isosceles triangle.
So far, we have a
right isosceles triangle.
---
Step 2: Classify based on side lengths
- Two sides are equal (4.8 and 4.8) →
isosceles
- One side is different (6.8) → not equilateral
- All angles are less than 90° except the right angle → not obtuse or acute overall
But since it has a
right angle, it’s
not acute.
So, the classification is:
>
Right isosceles triangle
---
Now, look at the choices:
A)
right isosceles →
✔
B) scalene isosceles →
✘ (scalene means all sides different; contradiction)
C) obtuse scalene →
✘ (no obtuse angle here)
D) acute scalene →
✘ (has a right angle, not acute)
---
✔ Final Answer: A) right isosceles
Parent Tip: Review the logic above to help your child master the concept of classify triangles by sides and angles worksheet.
