Describe the triangle ( $$ \triangle X Y Z $$, not shown) as scalene, isosceles, or equilateral. $$ \mathrm{m} \angle X=\mathrm{m}_{\angle} Y=24^{\circ} $$ scalene triangle isosceles triangle equilateral triangle Is the triangle acute, right, or obtuse? acute triangle right triangle obtuse triangle

Question

UpStudy AI · Accepted Answer

Given triangle $$ \triangle XYZ $$ with the following angle measures:
$$
\mathrm{m} \angle X = \mathrm{m} \angle Y = 24^{\circ}
$$

### Classification by Sides:
- **Isosceles Triangle**: 
  - A triangle is **isosceles** if at least two sides (and consequently, at least two angles) are equal.
  - Since $$ \angle X = \angle Y $$, sides $$ XY $$ and $$ XZ $$ (opposite these angles) are equal.
  - **Conclusion**: $$ \triangle XYZ $$ is an **isosceles triangle**.

### Classification by Angles:
1. **Determine the Third Angle**:
   $$
   \mathrm{m} \angle Z = 180^{\circ} - (\mathrm{m} \angle X + \mathrm{m} \angle Y) = 180^{\circ} - (24^{\circ} + 24^{\circ}) = 132^{\circ}
   $$
   
2. **Determine the Type of Triangle**:
   - **Acute Triangle**: All angles are less than $$ 90^{\circ} $$.
   - **Right Triangle**: One angle is exactly $$ 90^{\circ} $$.
   - **Obtuse Triangle**: One angle is greater than $$ 90^{\circ} $$.

- Since $$ \angle Z = 132^{\circ} > 90^{\circ} $$, $$ \triangle XYZ $$ has an **obtuse angle**.
   
   - **Conclusion**: $$ \triangle XYZ $$ is an **obtuse triangle**.

### Summary:
- **Type by Sides**: Isosceles Triangle
- **Type by Angles**: Obtuse Triangle
The triangle is an isosceles triangle and an obtuse triangle.

Describe the triangle ( \( \triangle X Y Z \), not shown) as scalene, isosceles, or equilateral. \[ \mathrm{m} \angle X=\mathrm{m}_{\angle} Y=24^{\circ} \] scalene triangle isosceles triangle equilateral triangle Is the triangle acute, right, or obtuse? acute triangle right triangle obtuse triangle

Solución de tutoría real

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions