Learn Ncert All Solutions

from a handpicked tutor in LIVE 1-to-1 classes

from a handpicked tutor in LIVE 1-to-1 classes

# In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

i) ar (ACB) = ar (ACF)

ii) ar (AEDF) = ar (ABCDE)

**Solution:**

i) ΔACB and ΔACF are lying on the same base AC and are existing between the same parallels AC and BF.

According to Theorem 9.2: Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Therefore, ar (ΔACB) = ar (ΔACF)

ii) It can be observed that

ar (ΔACB) = ar (ΔACF)

Adding area (ACDE) on both the sides.

Area (ΔACB) + Area (ACDE) = Area (ΔACF) + Area (ACDE)

Area (ABCDE) = Area (AEDF)

Hence proved.

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 9

**Video Solution:**

## In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that i) ar (ACB) = ar (ACF) ii) ar (AEDF) = ar (ABCDE)

Maths NCERT Solutions Class 9 Chapter 9 Exercise 9.3 Question 11

**Summary:**

If ABCDE is a pentagon, a line through B parallel to AC meets DC produced at F, then ar (ACB) = ar (ACF), and ar (AEDF) = ar (ABCDE).

**☛ Related Questions:**

- A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.
- ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).[Hint: Join CX.]
- In Fig.9.28, AP || BQ || CR. Prove that ar (AQC) = ar (PBR)
- Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

Math worksheets and

visual curriculum

visual curriculum