CBSE Class 7 Mathematics Triangle And Its Properties Worksheet Set 02

Question 1. Write the six elements (i.e. three sides and three angles) of \(\Delta ABC\).
Answer: The six elements of \(\Delta ABC\) are:
Three sides: \(AB\), \(BC\), and \(CA\)
Three angles: \(\angle ABC\), \(\angle BCA\), and \(\angle CAB\) (or \(\angle B\), \(\angle C\), and \(\angle A\))
In simple words: A triangle has 3 sides and 3 angles, making a total of 6 parts.

Exam Tip: Always list sides using two capital letters representing their endpoints, and angles using three letters with the vertex in the middle.

Question 2(i)(a). The side opposite to the vertex Q of \(\Delta PQR\) is _____
Answer: \(PR\)
In simple words: The side that does not touch vertex Q is PR.

Exam Tip: The side opposite to any vertex of a triangle is formed by the remaining two vertices.

Question 2(i)(b). The angle opposite to the side LM of \(\Delta LMN\) is _____
Answer: \(\angle N\) (or \(\angle LNM\))
In simple words: The angle formed at the vertex not part of side LM is angle N.

Exam Tip: The angle opposite to a given side is always the vertex letter that is missing from the side's name.

Question 2(i)(c). The vertex opposite the side RT of \(\Delta RST\) is _____
Answer: Vertex S
In simple words: The single point opposite line segment RT is S.

Exam Tip: Look at the three letters of the triangle name; the one not included in the side is the opposite vertex.

Question 2(ii)(a). Classify the triangles according Sides :-
Answer: Triangles are classified by their sides into three types:
1. Scalene triangle (all sides are of different lengths)
2. Isosceles triangle (two sides are of equal length)
3. Equilateral triangle (all three sides are of equal length)
In simple words: Triangles get names based on whether their sides are all different, two are equal, or all three are equal.

Exam Tip: Memorize the three side-based classifications along with their definitions.

Question 2(ii)(b). Classify the triangles according Angles
Answer: Triangles are classified by their angles into three types:
1. Acute-angled triangle (all three angles are acute, i.e., less than \(90^\circ\))
2. Right-angled triangle (one angle is exactly \(90^\circ\))
3. Obtuse-angled triangle (one angle is obtuse, i.e., greater than \(90^\circ\))
In simple words: Triangles are named acute, right, or obtuse depending on the size of their interior angles.

Exam Tip: A triangle can have at most one right angle or one obtuse angle.

Question 3(a). A triangle is a ________curve made of _____line______. It has ______vertices_____ angles and ________sides.
Answer: A triangle is a simple closed curve made of three line segments. It has three vertices, three angles and three sides.
In simple words: A triangle is a closed shape made of three straight lines, three corners, and three sides.

Exam Tip: Remember the basic definition and components of a polygon with the least number of sides.

Question 3(b). A median connects a vertex of a triangle to the _________of the __________side.
Answer: A median connects a vertex of a triangle to the midpoint of the opposite side.
In simple words: A median goes from a corner to the exact middle of the opposite side.

Exam Tip: Medians divide the opposite side into two equal halves.

Question 3(c). A triangle has ______medians
Answer: A triangle has three medians.
In simple words: Every triangle has three corners, so it has three medians.

Exam Tip: The three medians of a triangle always intersect at a single point called the centroid.

Question 3(d). An exterior angle of a triangle is equal to the ______of its _____________opposite _________.
Answer: An exterior angle of a triangle is equal to the sum of its interior opposite angles.
In simple words: An outside angle equals the addition of the two inside angles that are far away from it.

Exam Tip: This is known as the Exterior Angle Property of a triangle and is very useful in geometry proofs.

Question 3(e). The _________________line ______________ drawn from a vertex of a triangle to its ________ side is called an altitude of the triangle.
Answer: The perpendicular line segment drawn from a vertex of a triangle to its opposite side is called an altitude of the triangle.
In simple words: An altitude is a straight line dropped straight down at a \(90^\circ\) angle from a corner to the opposite side.

Exam Tip: Altitude means height, and it always makes a right angle (\(90^\circ\)) with the base.

Question 3(f). A triangle has ______altitudes.
Answer: A triangle has three altitudes.
In simple words: You can drop a perpendicular height from each of the three vertices.

Exam Tip: The intersection point of the three altitudes is called the orthocenter.

Question 3(g). The total measure of the three angles of a triangle is____.
Answer: The total measure of the three angles of a triangle is \(180^\circ\).
In simple words: If you add all three inside angles of any triangle, the sum is always \(180^\circ\).

Exam Tip: This is the Angle Sum Property of triangles, fundamental for finding missing angles.

Question 3(h). A triangle which has three sides equal is called an ___________________________________.
Answer: A triangle which has three sides equal is called an equilateral triangle.
In simple words: A triangle with all equal sides is equilateral.

Exam Tip: In an equilateral triangle, all three interior angles are also equal, each measuring \(60^\circ\).

Question 3(i). Each angle of an equilateral triangle is of measure _____.
Answer: Each angle of an equilateral triangle is of measure \(60^\circ\).
In simple words: Since all 3 angles are equal and add up to \(180^\circ\), each must be \(60^\circ\).

Exam Tip: \(180^\circ \div 3 = 60^\circ\).

Question 3(j). A triangle which has two sides equal is called an______________________________________________.
Answer: A triangle which has two sides equal is called an isosceles triangle.
In simple words: A triangle with a pair of equal sides is called isosceles.

Exam Tip: Remember that equal sides subtend equal angles opposite to them.

Question 3(k). The unequal side of an isosceles triangle is called its______.
Answer: The unequal side of an isosceles triangle is called its base.
In simple words: The side that is different in length from the other two is referred to as the base.

Exam Tip: The angles opposite to the equal sides are called the base angles.

Question 3(l). The base angles of an isosceles triangle are_______.
Answer: The base angles of an isosceles triangle are equal.
In simple words: The two angles adjacent to the base are always equal in measure.

Exam Tip: If two sides of a triangle are equal, their opposite angles are also equal.

Question 3(m). The sum of the lengths of any two sides of a triangle is____________ than the length of the third side.
Answer: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
In simple words: Adding any two sides together always gives a bigger number than the third side.

Exam Tip: This is known as the triangle inequality property: \(a + b > c\).

Question 3(n). The difference of the lengths of any two sides of a triangle is____________ than the length of the third side.
Answer: The difference of the lengths of any two sides of a triangle is less than the length of the third side.
In simple words: Subtracting one side from another gives a smaller result than the remaining third side.

Exam Tip: Expressed mathematically as \(|a - b| < c\).

Question 3(o). The longest side of a right angled triangle is the______.
Answer: The longest side of a right-angled triangle is the hypotenuse.
In simple words: The side opposite to the right angle is always the longest side and is called the hypotenuse.

Exam Tip: The hypotenuse is always opposite the \(90^\circ\) angle.

Question 3(p). The longest side in \(\Delta PQR\), right angled at P is _______.
Answer: QR
In simple words: Since angle P is the right angle, the side opposite to P is QR, which is the hypotenuse and the longest side.

Exam Tip: The side formed by the two letters other than the right-angled vertex is always the hypotenuse.