shaalaa.com
S

Solution - Triangles on the Same Base and Between the Same Parallels

Account
User


Login
Register


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty
ConceptTriangles on the Same Base and Between the Same Parallels  

Question

In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:

(i) ar (DOC) = ar (AOB)

(ii) ar (DCB) = ar (ACB)

(iii) DA || CB or ABCD is a parallelogram.

[Hint: From D and B, draw perpendiculars to AC.]

Solution

You need to to view the solution
Is there an error in this question or solution?

Similar questions VIEW ALL

D and E are points on sides AB and AC respectively of ΔABC such that

ar (DBC) = ar (EBC). Prove that DE || BC.

view solution

In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that

(i) ar (BDE) = 1/4 ar (ABC)

(ii) ar (BDE) = 1/2 ar (BAE)

(iii) ar (ABC) = 2 ar (BEC)

(iv) ar (BFE) = ar (AFD)

(v) ar (BFE) = 2 ar (FED)

(vi) ar (FED) = 1/8 ar (AFC)

[Hint : Join EC and AD. Show that BE || AC and DE || AB, etc.]

view solution

In the given figure, AP || BQ || CR. Prove that ar (AQC) = ar (PBR).

view solution

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that

(i) BDEF is a parallelogram.

(ii) ar (DEF) = 1/4ar (ABC)

(iii) ar (BDEF) = 1/2ar (ABC)

view solution

XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that

ar (ABE) = ar (ACF)

view solution

Content BooksVIEW ALL [1]

BooksVIEW ALL [1]

Solution for concept: Triangles on the Same Base and Between the Same Parallels. For the course 8th-10th CBSE
S