Daily Practice Problems undefined Similarity (With Applications to Maps and Models)

Question 1:

E and F are the points in sides DC and AB respectively of parallelogram ABCD. If diagonal AC and segment EF intersect at G; prove that: AG × EG = FG × CG [Level: Easy]

Question 2:

Given: FB = FD, AE ⊥ FD and FC ⊥ AD .

Prove: [Level: Moderate]

Question 3:

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that AE: EC = BE: ED . Show that ABCD is a parallelogram. [Level: Moderate]

Question 4:

In triangle ABC, AD is perpendicular to side BC and = BD × DC. Show that angle BAC = 90° [Level: Moderate]

Question 5:

In the right-angled triangle QPR, PM is an altitude. Given that QR = 8cm and MQ = 3.5 cm, calculate the value of PR. [Level: Moderate]

Question 6:

The ratio between the corresponding sides of two similar triangles is 2 is to 5. Find the ratio between the areas of these triangles. [Level: Easy]

Question 7:

The perimeter of two similar triangles are 30 cm and 24 cm. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle. [Level: Moderate]

Question 8:

On a map, drawn to a scale of 1 : 250000, a triangular plot PQR of land has the following measurements : PQ = 3cm, QR = 4 cm and angles PQR = 90° . Calculate the actual lengths of QR and PR in kilometer. [Level: Difficult]

Question 9:

The two similar triangles are equal in area. Prove that the triangles are congruent. [Level: Difficult]

Question 10:

The following figure shows a triangle PQR in which XY is parallel to QR. If PX : XQ = 1 : 3 and QR = 9 cm. Find the length of XY. [Level: Moderate]

Question 11:

In ∆ABC, ∠ACB = 90° and CD ⊥ AB. Prove that : = . [Level: Difficult]

Question 12:

In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively. Prove: ∆ADE ~ ∆ABC. Also, find the length of DE, if AD = 12 cm, BD = 24 cm BC = 8 cm. [Level: Moderate]

Question 13:

ABCD is a rhombus, DRP and CBR are straight lines. Prove that: DP × CR = DC × PR. [Level: Moderate]

Question 14:

In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10cm, L is a point on PR such that RL: LP = 2: 3. QL produced meets RS at M and PS produced at N. Find the lengths of PN and RM.

[Level: Difficult]

Question 15:

In ∆PQR, ∠Q = 90° and QM is perpendicular to PR. Prove that: = PM × PR. [Level: Easy]

Question 16:

In the given figure, QR is parallel to AB and DR is parallel to AB and DR is parallel to QB. Prove that: = PD × PA. [Level: Moderate]

Question 17:

Area of two similar triangles are 98 sq.cm and 128 sq.cm. Find the ratio between the lengths of their corresponding sides. [Level: Easy]

Question 18:

ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ ∥ BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP : AB. [Level: Moderate]

Question 19:

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ. Calculate the length of AP. [Level: Easy]

Question 20:

In the given figure, ∠B = ∠E, ∠ACD = ∠BCE, AB = 10.4cm and DE = 7.8 cm. Find the ratio between areas of the ∆ABC and ∆ DEC. [Level: Moderate]

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Problem-solving on ICSE 10 Maths Similarity (With Applications to Maps and Models) NCERT Chapter 15 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic ICSE 10 Maths Similarity (With Applications to Maps and Models) you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in ICSE 10 Maths Similarity (With Applications to Maps and Models) NCERT Chapter 15, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Similarity (With Applications to Maps and Models) ICSE 10 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Similarity (With Applications to Maps and Models) ICSE 10 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Similarity (With Applications to Maps and Models). This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Similarity (With Applications to Maps and Models) ICSE 10 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Similarity (With Applications to Maps and Models) ICSE 10 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on ICSE 10 Maths Similarity (With Applications to Maps and Models) NCERT Chapter 15

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on ICSE 10 Maths Similarity (With Applications to Maps and Models) NCERT Chapter 15 useful.

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