CBSE Class 7 Mathematics Triangles and Its Properties Assignment Set 11

Question 1. How many points are needed to construct a triangle?
Answer: We need exactly 3 points to construct a triangle. These three points must be non-collinear, which means they do not lie on the same straight line.
In simple words: You need three points that are not in a straight line to make a triangle.
Exam Tip: Remember that if the three points are in a single straight line, they cannot form a triangle.

Question 2. Take three non collinear points P, Q, R on the page of your note book. Join PQ, QR and RP. Is the figure a triangle? If yes state the type and if No then explain why?
Answer: Yes, the shape formed by joining these points is a triangle. It is generally a scalene triangle because the three points are taken randomly, so all three sides will usually have different lengths.

In simple words: Yes, joining three points that are not in a straight line always makes a triangle. It is usually a scalene triangle because its sides have different lengths.

Exam Tip: Always make sure to label the vertices of the triangle with capital letters P, Q, and R as requested in the question.

Question 3. Can you draw a triangle with three collinear points? If No why?
Answer: No, it is impossible to draw a triangle using three collinear points. This is because all three points lie on the same straight line, so joining them will only produce a single straight line instead of a closed three-sided shape.
In simple words: No, if all three points are in a straight line, joining them just makes one long line instead of a triangle.

Exam Tip: A triangle requires three non-collinear points because collinear points will always lie on a single straight line.

Question 4. From the \( \Delta PQR \), answer the following questions.
(a) side opposite to \( \angle R \)
(b) Angle opposite to side QR
(c) vertex opposite to side RP
(d) Side opposite to the vertex P
Answer:
(a) The side opposite to \( \angle R \) is PQ.
(b) The angle opposite to side QR is \( \angle P \).
(c) The vertex opposite to side RP is Q.
(d) The side opposite to vertex P is QR.

In simple words: To find an opposite side, angle, or corner, just look straight across from the given part in the triangle diagram.

Exam Tip: A quick shortcut is that the side opposite to a vertex does not contain that vertex's letter in its name (for example, the side opposite to P is QR).

Question 5. What is the difference between a triangle and triangular region
Answer: A triangle is simply the boundary line made of three straight segments. In contrast, a triangular region includes both this boundary line and all the flat space enclosed inside it.
In simple words: A triangle is just the outer outline, while the triangular region is the outline plus all the space inside it.

Exam Tip: Remember that any point on the boundary is part of both the triangle and the triangular region, but a point inside is only part of the triangular region.

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Question 6. From the adjoining figure, find the total different types of triangles and name them.
Answer: There are 11 different triangles in total in this figure. Their names are as follows:
1. \( \Delta ABC \)
2. \( \Delta ABE \)
3. \( \Delta ACD \)
4. \( \Delta ADE \)
5. \( \Delta DEF \)
6. \( \Delta DBF \)
7. \( \Delta EFC \)
8. \( \Delta DEB \)
9. \( \Delta DEC \)
10. \( \Delta DBC \)
11. \( \Delta FBC \)

In simple words: If you count every three-sided shape inside the big drawing, you will find exactly 11 triangles.

Exam Tip: When counting triangles in a complex figure, group them systematically by size - starting from the smallest single triangles and then moving to larger combined triangles - to avoid missing any.

Question 7. Explain with the help of figure, the Scalene, isosceles or equilateral \( \Delta \)s.
Answer: We can group triangles into three types based on the lengths of their sides:
1. Scalene Triangle: A triangle where all three sides have completely different lengths.
2. Isosceles Triangle: A triangle that has two sides of equal length.
3. Equilateral Triangle: A triangle where all three sides are exactly equal in length.

In simple words: A scalene triangle has sides of all different sizes, an isosceles triangle has two sides that are the same, and an equilateral triangle has three sides that are exactly the same.

Exam Tip: In diagrams, use small tick marks on the sides to show which sides are equal to each other.

Question 8. How many medians a triangle have? Explain with the help of diagram.
Answer: Every triangle has exactly 3 medians. A median is a line segment that joins any vertex of the triangle to the midpoint of its opposite side. In the diagram below, AD, BE, and CF are the three medians of the triangle ABC.

In simple words: A median is a line drawn from a corner of a triangle to the exact middle of the opposite side. Every triangle has three medians.

Exam Tip: Always show that the median bisects the opposite side by marking the two halved segments with identical markers.

Question 9. The point of intersection of three medians is called by _________ and it divides the medians in the ratio _________
Answer: The point of intersection of three medians is called the Centroid, and it divides the medians in the ratio 2:1.
In simple words: The spot where all three medians cross each other is called the centroid. This point splits each median line so that the segment closer to the corner is twice as long as the other segment.

Exam Tip: Remember that the ratio 2:1 always starts from the vertex (corner) to the opposite side's midpoint.

Question 10. Define altitude of a \( \Delta \). How many altitudes a \( \Delta \) have? Name the point of intersection of altitudes.
Answer:
1. Altitude: An altitude is a perpendicular line segment drawn from a vertex of a triangle to its opposite side.
2. Every triangle has exactly 3 altitudes.
3. The point where all three altitudes intersect is called the Orthocentre.

In simple words: An altitude is a straight height line from a corner of a triangle that meets the opposite side at a 90-degree corner. Every triangle has three altitudes, and they all meet at the orthocentre.

Exam Tip: Be careful - unlike medians, altitudes do not always bisect the opposite sides unless the triangle is equilateral or isosceles.