RS Aggarwal Solutions Class 7 Chapter-15 Properties of Triangles (Ex 15A) Exercise 15.1 - Free PDF
FAQs on RS Aggarwal Solutions Class 7 Chapter-15 Properties of Triangles (Ex 15A) Exercise 15.1
1. How do I solve for the third angle of a triangle in RS Aggarwal Ex 15A when two angles are given?
To find the third angle, you must use the angle sum property of a triangle. This property states that the sum of all three interior angles in any triangle is always 180°.
The correct method is:
1. Add the measures of the two given angles.
2. Subtract this sum from 180°.
3. The result is the measure of the third angle. For example, if two angles are 50° and 70°, their sum is 120°. The third angle would be 180° - 120° = 60°.
2. What is the step-by-step method to find the angles of a triangle when they are given in a ratio, as in some questions in Exercise 15.1?
When angles are in a ratio (e.g., 2:3:4), follow these steps:
- Step 1: Represent the angles using a common variable 'x'. For a ratio of 2:3:4, the angles would be 2x, 3x, and 4x.
- Step 2: Apply the angle sum property. Write the equation: 2x + 3x + 4x = 180°.
- Step 3: Solve the equation for x. In this case, 9x = 180°, so x = 20°.
- Step 4: Substitute the value of x back to find each angle. The angles would be 2(20°) = 40°, 3(20°) = 60°, and 4(20°) = 80°.
3. How do you apply the exterior angle property to solve problems in this chapter?
The exterior angle property states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two opposite interior angles. To apply it, identify the exterior angle and the two interior angles that are not adjacent to it. For instance, if an exterior angle is 110° and one of the opposite interior angles is 50°, the other opposite interior angle must be 110° - 50° = 60°.
4. What is a common mistake to avoid when finding angles in an isosceles triangle?
A common mistake is incorrectly identifying the equal angles. In an isosceles triangle, the angles opposite the equal sides are equal, not just any two angles. Always identify which sides are equal first, then find the angles opposite to them. For example, if sides AB and AC are equal, then the angles opposite them, ∠C and ∠B, will be equal.
5. Why is it impossible for a triangle to have two right angles or two obtuse angles?
This is because of the angle sum property. A right angle is 90° and an obtuse angle is greater than 90°.
- Two right angles: The sum would be 90° + 90° = 180°. This leaves 0° for the third angle, which cannot form a triangle.
- Two obtuse angles: The sum would be greater than 90° + 90°, so their sum alone would exceed 180°. This violates the rule that the total sum of all three angles must be exactly 180°.
6. How are the concepts of an altitude and a median different, and why does it matter?
While both are lines drawn from a vertex, they have different purposes.
- An altitude is a line segment from a vertex that is perpendicular (forms a 90° angle) to the opposite side. It represents the height of the triangle.
- A median is a line segment from a vertex to the midpoint of the opposite side. It divides the opposite side into two equal lengths.
7. When solving a problem in Ex 15A, how do I decide whether to use the Angle Sum Property or the Exterior Angle Property?
The choice depends on the information given in the problem:
- Use the Angle Sum Property when you are dealing with all three interior angles of a triangle. This is the correct method if you know two inside angles and need to find the third.
- Use the Exterior Angle Property when the problem involves an angle formed outside the triangle by extending one of its sides. This property connects the exterior angle to the two opposite interior angles.
