Advertisements
Advertisements
प्रश्न
In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
Advertisements
उत्तर
In ΔQLM and ΔRNM
QM = MR
LM = MN
∠QLM = ∠RNM = 90°
Therefore, ΔQLM ≅ ΔRNM ...(RHS criteria)
Hence, QL = RN ..........(i)
Join PM
In ΔPLM and ΔPNM and
PM = PM ...(common)
LM = MN
∠PLM = ∠PNM = 90°
Therefore, ΔPLM ≅ ΔPNM ...(RHS criteria)
Hence, PL = PN ..........(ii)
From (i) and (ii)
PQ = PR.
APPEARS IN
संबंधित प्रश्न
Complete the congruence statement:
ΔBCA ≅?
ΔQRS ≅?
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that: LN = MN.
In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
ΔXYZ ≅ ΔLMN
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
If the following pair of the triangle is congruent? state the condition of congruency :
In ΔABC and ΔDEF, ∠B = ∠E = 90o; AC = DF and BC = EF.
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: ΔAMC≅ ΔANB
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Prove that:
- ∆ ABD ≅ ∆ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
Prove that in an isosceles triangle the altitude from the vertex will bisect the base.
