Advertisements
Advertisements
प्रश्न
A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.
Advertisements
उत्तर
Given: A ΔABQ in which AB is bisected at P
PQ is perpendicular to AB
We need to prove that
QA = QB
Proof:
In ΔAPQ and ΔBPQ
AP = PB ...[ P is the mid-point of AB ]
∠QPA = ∠QPB = 90° ...[ PQ is perpendicular to AB ]
PQ = PQ ...[ Common]
∴ By Side-Angel-Side criterion of congruence,
ΔQAP ≅ ΔQBP
The corresponding parts of the congruent triangles are
congruent.
∴ QA = QB ...[ c.p.c.t ]
APPEARS IN
संबंधित प्रश्न
AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.
AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that
- ΔDAP ≅ ΔEBP
- AD = BE
Explain, why ΔABC ≅ ΔFED.
In Δ ABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in P. Arrange AP, BP and CP in descending order.
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
The following figure shows a circle with center O.
If OP is perpendicular to AB, prove that AP = BP.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB = CE.
ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such produced to E and F respectively, such that AB = BE and AD = DF.
Prove that: ΔBEC ≅ ΔDCF.
ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.
