Extra Curriculum Support
Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
1.Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
2.Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
3.Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
4.Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1.The value of x in the following triangle is
(a) 6cm (b) 8cm (c) 5cm (d) 2cm
2.Name the pair of congruent triangles in the given figure.
(a) ΔABC ≅ ΔPQR
(b) ΔABC ≅ ΔRQP
(c) ΔBAC ≅ ΔPQR
(d) None of these
Sec B
1.In the figure below, ΔCDE ≅ ΔQPR. What is m∠D?
2. Explain ASA congruence condition with the help of a diagram.
Sec C
1. The lengths of two sides of a triangle are 6 cm and 8 cm. Between which two numbers can length of the third side fall?
2. In Fig, AB = AC and AD is the bisector of ∠BAC.
(i) State three pairs of equal parts in triangles ADB and ADC.
(ii) Is ΔADB ≅ ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Give reasons.
Sec D
1. Town A is 60 km from town B, and 61 km from town C. A road connects towns B and C directly. Find the length of this road.
Value-Based Questions
Problem 1
During a community project, a group of students is tasked with building a small triangular garden. They need to ensure that the garden’s design adheres to the properties of triangles, specifically that the sum of the angles in the triangle must be 180°. If they measure two angles of the triangle as 60° and 50°, how should they determine the measure of the third angle? Discuss how understanding geometric properties helps in practical applications like designing community projects.
Problem 2
A school plans to build a new playground that includes several triangular play structures. The designer needs to ensure that the playground is safe and well-constructed by applying the property that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If one of the play structures has sides of lengths 4 meters and 5 meters, what is the maximum length the third side can be to maintain safety? Why is it important to adhere to geometric properties in construction?
Problem 3
In a geometry competition, students are asked to find the area of a triangular park. They are given that the base of the triangle is 12 meters and the height from the base to the opposite vertex is 8 meters. How can they calculate the area of the park, and why is it important to accurately calculate areas in real-life scenarios such as planning public spaces?
HOTS
Q1
In a triangle, the sum of the lengths of two sides is always greater than the length of the third side. Suppose you are given a triangle with sides of lengths 7 cm, 10 cm, and 15 cm. Prove whether this set of side lengths can form a triangle. Additionally, if the side lengths were changed to 7 cm, 10 cm, and 18 cm, what would be the result, and why?
Q2
A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. Find the type of triangle it is based on its side lengths and explain why this classification is significant. Furthermore, if the same triangle was rotated 180°, how would this affect its classification and properties?
Q3
In a triangle, the angles are in the ratio 2 : 3 : 4. Calculate the angles of the triangle and determine the type of triangle based on the angle measurements. Additionally, if one of the angles is increased by 10°, how will this affect the type of triangle, and what geometric principles are involved in this change?
NCERT Exemplar Solutions
Questions
1. Which of the following cannot be the sides of a triangle?
(a) 3 cm, 4 cm, 5 cm
(b) 2 cm, 4 cm, 6 cm
(c) 2.5 cm, 3.5 cm, 4.5 cm
(d) 2.3 cm, 6.4 cm, 5.2 cm
2. The line segment joining a vertex of a triangle to the mid-point of its opposite side is called its ?
3. Sum of any two sides of a triangle is not less than the third side.
4. The measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.
5. The sides of a triangle have lengths (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is.
(a) 6 (b) 5 (c) 3 (d) 4
6. Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is.
(a) Obtuse angled triangle
(b) Acute-angled triangle
(c) Right-angled triangle
(d) An Isosceles right triangle
7. If in an isosceles triangle, each of the base angles is 40°, then the triangle is.
(a) Right-angled triangle
(b) Acute angled triangle
(c) Obtuse angled triangle
(d) Isosceles right-angled triangle
8. The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is.
(a) 120 cm (b) 122 cm (c) 71 cm (d) 142 cm
9. In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is
(a) 55° (b) 40° (c) 50° (d) 45°
10. The difference between the lengths of any two sides of a triangle is smaller than the length of third side.
11. It is possible to have a triangle in which each angle is less than 60°.
12. If the areas of two squares is same, they are congruent.
13. If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.
14. If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
15. Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
16. The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is 10°,find the three angles.
17. Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.
18. The lengths of two sides of an isosceles triangle are 9 cm and 20 cm.What is the perimeter of the triangle? Give reason.
19. If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?
20. Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.
Case-Based Questions
Q1
Engineers are constructing a triangular bridge with sides measuring 7 meters, 24 meters, and 25 meters. They need to determine whether this triangle is a right-angled triangle to ensure stability.
Question: Verify if the triangle is a right-angled triangle using the Pythagoras theorem. Explain your solution.
Q2
A gardener is designing a triangular flower bed in a park. The angles of the triangle are in the ratio 2 : 3 : 5.
Question: Determine the measure of each angle in the triangle and check if it forms a valid triangle. Justify your answer using the angle sum property of a triangle.
Q3
A flagpole casts a shadow of 12 meters. At the same time, a 1.5-meter stick placed vertically on the ground casts a shadow of 2 meters. Both the flagpole and the stick form right-angled triangles with the ground.
Question: Determine the height of the flagpole using the properties of similar triangles. Explain how you applied the concept of similar triangles to find the height.