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.