Properties of Shapes | 5th Grade Geometry Worksheets - Free Printable

Problem Description:

The task involves checking the properties of shapes listed in the table and determining whether each property applies to the shape in question. The shapes provided are:

1. Right Triangle
2. Equilateral Triangle
3. Scalene Triangle

We need to analyze each shape based on the given properties and mark the appropriate boxes.

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Solution:

#### 1. Right Triangle
- Properties:
- One angle is 90°.
- Two sides are perpendicular.
- No angles are 90°.
- Opposite angles are congruent.
- All angles are 60°.
- All sides are the same length.
- All sides are congruent.
- No sides are the same length.

- Analysis:
- A right triangle has one angle that is exactly 90°, so the first property ("One angle is 90°") is true.
- Since one angle is 90°, the two sides forming this angle are perpendicular, so the second property ("Two sides are perpendicular") is true.
- The third property ("No angles are 90°") is false because a right triangle does have one 90° angle.
- The fourth property ("Opposite angles are congruent") is irrelevant for a triangle (it applies to quadrilaterals like parallelograms).
- The fifth property ("All angles are 60°") is false because a right triangle cannot have all angles equal to 60° (the sum of angles in a triangle is 180°, and one angle is already 90°).
- The sixth property ("All sides are the same length") is false because a right triangle does not have all sides equal.
- The seventh property ("All sides are congruent") is false for the same reason as above.
- The eighth property ("No sides are the same length") is also false because a right triangle can have two sides of equal length (e.g., an isosceles right triangle).

- Marked Properties:
- One angle is 90°: ✔
- Two sides are perpendicular: ✔

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#### 2. Equilateral Triangle
- Properties:
- One angle is 90°.
- Two sides are perpendicular.
- No angles are 90°.
- Opposite angles are congruent.
- All angles are 60°.
- All sides are the same length.
- All sides are congruent.
- No sides are the same length.

- Analysis:
- An equilateral triangle has all three angles equal to 60°, so the first property ("One angle is 90°") is false.
- Since no angle is 90°, the sides are not perpendicular, so the second property ("Two sides are perpendicular") is false.
- The third property ("No angles are 90°") is true because none of the angles in an equilateral triangle are 90°.
- The fourth property ("Opposite angles are congruent") is irrelevant for a triangle.
- The fifth property ("All angles are 60°") is true because all angles in an equilateral triangle are 60°.
- The sixth property ("All sides are the same length") is true because all sides in an equilateral triangle are equal.
- The seventh property ("All sides are congruent") is true for the same reason as above.
- The eighth property ("No sides are the same length") is false because all sides in an equilateral triangle are equal.

- Marked Properties:
- No angles are 90°: ✔
- All angles are 60°: ✔
- All sides are the same length: ✔
- All sides are congruent: ✔

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#### 3. Scalene Triangle
- Properties:
- One angle is 90°.
- Two sides are perpendicular.
- No angles are 90°.
- Opposite angles are congruent.
- All angles are 60°.
- All sides are the same length.
- All sides are congruent.
- No sides are the same length.

- Analysis:
- A scalene triangle has no sides or angles equal. Therefore:
- The first property ("One angle is 90°") could be true if the scalene triangle happens to be a right triangle, but it is not guaranteed.
- The second property ("Two sides are perpendicular") could also be true if the scalene triangle is a right triangle, but it is not guaranteed.
- The third property ("No angles are 90°") is true if the scalene triangle is not a right triangle.
- The fourth property ("Opposite angles are congruent") is irrelevant for a triangle.
- The fifth property ("All angles are 60°") is false because a scalene triangle does not have all angles equal to 60°.
- The sixth property ("All sides are the same length") is false because a scalene triangle does not have all sides equal.
- The seventh property ("All sides are congruent") is false for the same reason as above.
- The eighth property ("No sides are the same length") is true because a scalene triangle has no sides of equal length.

- Marked Properties:
- No angles are 90°: ✔ (if not a right triangle)
- No sides are the same length: ✔

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Final Answer:

- Right Triangle:
- One angle is 90°: ✔
- Two sides are perpendicular: ✔

- Equilateral Triangle:
- No angles are 90°: ✔
- All angles are 60°: ✔
- All sides are the same length: ✔
- All sides are congruent: ✔

- Scalene Triangle:
- No angles are 90°: ✔ (if not a right triangle)
- No sides are the same length: ✔

$$
\boxed{
\text{See marked properties above.}
}
$$