Equal-area theorems, base-altitude reasoningPractice Questions & MCQs
Practice Equal-area theorems, base-altitude reasoning questions from Areas of Parallelograms and Triangles (Class 9 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Equal-area theorems, base-altitude reasoningQuiz - Solve & Score
Q1. ABCD is a parallelogram. P is any point on diagonal BD. Triangles APD and CPD are compared. Which statement is true?
- A.ar(APD) = ar(CPD)
- B.ar(APD) = 2·ar(CPD)
- C.ar(APD) = (1/2)·ar(CPD)
- D.They are unequal in general
Answer: A. ar(APD) = ar(CPD)
NCERT fact (math, chapter 'Areas of Parallelograms and Triangles'): BD is a diagonal of parallelogram ABCD, so ar(ABD) = ar(CBD). Subtracting ar(BPD) from both equal areas (since P lies on BD, BPD is common to triangles ABD and CBD when viewed correctly), or directly: triangles APD and CPD share base PD and have equal heights from A and C to line BD because diagonals bisect the parallelogram. Hence ar(APD) = ar(CPD). Final answer - A) ar(APD) = ar(CPD).
Q2. Triangle ABC has area 90. Points D, E lie on BC with BD = DE = EC. Lines AD and AE divide the triangle into three smaller triangles. Which statement is true?
- A.All three have equal area 30
- B.Areas are 20, 30, 40
- C.Areas are 15, 30, 45
- D.Areas are 22.5, 45, 22.5
Answer: A. All three have equal area 30
Q3. In a triangle ABC, the medians AD, BE, CF intersect at G. ar(AGF) equals what fraction of ar(ABC)?
- A.1/6
- B.1/3
- C.1/4
- D.1/12
Answer: A. 1/6
Start by listing the data - the numerical data stated in the question (math, chapter 'Areas of Parallelograms and Triangles'). What we must find: the requested quantity. The principle that connects these is - So ar(AGF) = (1/6)·ar(ABC). Substituting and simplifying: So ar(AGF) = (1/6)·ar(ABC). The three medians of a triangle divide it into 6 smaller triangles of equal area. That lands on option A) 1/6.
Master Equal-area theorems, base-altitude reasoning on RankByte
Step-by-step solutions, mock tests, live ranks and streaks - free to start.
Get early accessEqual-area theorems, base-altitude reasoning - Frequently asked questions
Where can I practise Equal-area theorems, base-altitude reasoning questions for Class 9 Maths?
RankByte has Equal-area theorems, base-altitude reasoning practice questions and MCQs from Areas of Parallelograms and Triangles (Class 9 Maths), each with the correct answer and a step-by-step solution - free to start.
Are these Equal-area theorems, base-altitude reasoning questions important for the exam?
Yes. These Equal-area theorems, base-altitude reasoning important questions follow the Maths exam pattern (CBSE Boards, plus JEE and NEET foundation), so they help with both school and competitive prep.
Do the Equal-area theorems, base-altitude reasoning questions come with answers and solutions?
Every Equal-area theorems, base-altitude reasoning question on RankByte comes with the correct answer and a full step-by-step solution, so you learn the concept instead of just guessing.