Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.3, 14 Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ABC PQR. Given: ABC and PQR AD is the median of ABC ,PM is the median of PQR / = / = / To Prove:- ABC PQR. Proof: Let us extend AD to point D such that AD = DE and PM up to point L such that PM = ML Join B to E, C to E, & Q to L, and R to L We know that medians is the bisector of opposite side Hence, BD = DC Also, AD = DE Hence in quadrilateral ABEC, diagonals AE and BC bisect each other at point D. Therefore, quadrilateral ABEC is a parallelogram. AC = BE and AB = EC Similarly, we can prove that PQLR is a parallelogram PR = QL, PQ = LR Given that / = / = / / = / = / / = / =2 /2 / = / = / ABE PQL ABE PQL We know that corresponding angles of similar triangles are equal. BAE = QPL Similarly, we can prove that AEC PLR We know that corresponding angles of similar triangles are equal. CAE = RPL Adding (4) & (5), BAE + CAE = QPL + RPL CAB = RPQ In ABC and PQR, / = / CAB = RPQ ABC PQR Hence proved

Example 5
Important

Example 8 Important

Example 10 Important

Example 14 Important

Theorem 6.1 - Basic Proportionality Theorem (BPT) Important

Theorem 6.7 Important

Ex 6.2, 4 Important

Ex 6.2, 5 Important

Ex 6.2, 6 Important

Ex 6.2, 9 Important

Ex 6.3, 11 Important

Ex 6.3, 12 Important

Ex 6.3, 13 Important

Ex 6.3, 14 Important You are here

Ex 6.3, 15 Important

Ex 6.4, 1 Important

Ex 6.4, 3 Important

Ex 6.4, 5 Important

Ex 6.5, 2 Important

Ex 6.5, 3 Important

Ex 6.5, 8 Important

Ex 6.5, 11 Important

Ex 6.5, 12 Important

Ex 6.5, 15 Important

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.