**Properties of Triangles – Maharashtra Board Class 7 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

**Exercise 1:**

**Solution 1:**

In ΔABC,

- Segment CD is the altitude on side AB.
- Segment AF is the altitude on side BC.
- Segment BE is the altitude on side AC.

**Solution 2:**

- In ΔKLP, seg KN is an
__altitude__. - In ΔKLP, seg KM is a
__median__.

**Solution 3:**

- Point D is the midpoint of seg VW.
- l(VW) = 2 × l(VD) = 2 × 5 = 10 cm

**Solution 4:**

Yes, segment PD can be the altitude as well as the median of ΔPQR.

**Reason:
**Given, segment PD is the perpendicular drawn from vertex P to the opposite side QR.

D is the midpoint of segment QR. So, PD is the median of ΔPQR.

∴ Segment PD is the median as well as the altitude of ΔPQR.

**Solution 5:**

**Solution 6:**

The median is the line segment joining the vertex of a triangle and the midpoint of its opposite side.

Steps of construction:

- Draw any ΔXYZ.
- Construct the bisector of each side of the triangle to find the midpoints of each of the sides of ΔXYZ.
- Hence, P, Q and R are the midpoints of the sides XY, YZ and ZX of ΔXYZ respectively.
- Join the vertex X to the midpoint Q of its opposite side YZ.
- Similarly, join R and Y, P and Z.

Thus, seg XQ, seg YR and seg ZP are the three medians of ΔXYZ.

**Solution 7:**

The angle bisectors divide the given angle into two equal angles.

Steps of construction:

- Draw any ΔSTD.
- Construct the angle bisectors of each of the angles of ΔSTD.

Hence, SY, DX and TZ are the three angle bisectors of ΔSTD.

**Solution 8:**

- Draw any ΔCID.
- Construct the perpendicular bisectors of each of the sides of ΔCID.

Thus, seg DZ, seg CX and seg IY are the three perpendicular bisectors of ΔCID.

**Solution 9:**

**Steps of construction:**

- Draw any ΔRTO.
- Construct the perpendicular bisectors of each of the sides of the triangle to find the midpoint of each of the sides of ΔRTO.
- Hence, A, C and E are the midpoints of the sides TR, RO and OT of ΔRTO.
- Construct the perpendicular bisectors from the midpoints of the three sides of ΔRTO.

Hence, AB, FE and CD are the three perpendicular bisectors of ΔRTO.

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