Advertisements
Advertisements
प्रश्न
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).
Advertisements
उत्तर
In ΔABC and ΔPQR
∠B = ∠Q
BC = PQ
By Pythagoras theorem,
PR2 = PQ2 + QR2
102 = 62 + QR2
100 = 36 + QR2
QR = `sqrt(100 - 36)`
QR = `sqrt(64)` = 8cm
AB = QR
Therefore,
ΔABC ≅ ΔPQR ...(SAS criteria).
APPEARS IN
संबंधित प्रश्न
In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC.
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 triangles in each pair are congruent.
By ______ test
ΔPRQ ≅ ΔSTU
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.
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
State, whether the pairs of triangles given in the following figures are congruent or not:
In the given figure, prove that:
(i) ∆ ACB ≅ ∆ ECD
(ii) AB = ED
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).
Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.
∆ABC and ∆PQR are congruent under the correspondence:
ABC ↔ RQP
Write the parts of ∆ABC that correspond to
(i) `bar"PQ"`
(ii)∠Q
(iii) `bar"RP"`
