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प्रश्न
State the midpoint theorem
उत्तर
The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is equal to one half of the third side.
APPEARS IN
संबंधित प्रश्न
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.
In a ΔABC, P and Q are points on sides AB and AC respectively, such that PQ || BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If` (AD)/(AB) = 8/15 and EC = 3.5cm`, find AE.
An aeroplane leaves an airport and flies due north at a speed of 1000km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after` 1 1/2` hours?
In triangle BMP and CNR it is given that PB= 5 cm, MP = 6cm BM = 9 cm and NR = 9cm. If ΔBMP∼ ΔCNR then find the perimeter of ΔCNR
Prove that, if a line parallel to a side of a triangle intersects the other sides in two district points, then the line divides those sides in proportion.
In ΔPQR, NM || RQ. If PM = 15, MQ = 10, NR = 8, then find PN.
In fig., line BC || line DE, AB = 2, BD = 3, AC = 4 and CE = x, then find the value of x
A line is parallel to one side of triangle which intersects remaining two sides in two distinct points then that line divides sides in same proportion.
Given: In ΔABC line l || side BC and line l intersect side AB in P and side AC in Q.
To prove: `"AP"/"PB" = "AQ"/"QC"`
Construction: Draw CP and BQ
Proof: ΔAPQ and ΔPQB have equal height.
`("A"(Δ"APQ"))/("A"(Δ"PQB")) = (["______"])/"PB"` .....(i)[areas in proportion of base]
`("A"(Δ"APQ"))/("A"(Δ"PQC")) = (["______"])/"QC"` .......(ii)[areas in proportion of base]
ΔPQC and ΔPQB have [______] is common base.
Seg PQ || Seg BC, hence height of ΔAPQ and ΔPQB.
A(ΔPQC) = A(Δ______) ......(iii)
`("A"(Δ"APQ"))/("A"(Δ"PQB")) = ("A"(Δ "______"))/("A"(Δ "______"))` ......[(i), (ii), and (iii)]
`"AP"/"PB" = "AQ"/"QC"` .......[(i) and (ii)]
Find the value of x for which DE || AB in figure.
