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प्रश्न
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
उत्तर
In ∆DHC and ∆DFC,
∠DCH ≅ ∠DCF (given)
∠DHC ≅ ∠DFC (given)
side DC is common
∴ By AAS test, ∆DHC ≅ ∆DFC.
∴ side DH ≅ side DF,
side HC ≅ side FC,
∠HDC ≅ ∠FDC.
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
In a squared sheet, draw two triangles of equal areas such that
The triangles are not congruent.
What can you say about their perimeters?
In the given figure, the measure of ∠B'A'C' is
ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
∴ ΔABC ≅ ΔPQR ...`square` test
∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent triangles
State, whether the pairs of triangles given in the following figures are congruent or not:
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
In the figure, ∠CPD = ∠BPD and AD is the bisector of ∠BAC. Prove that ΔCAP ≅ ΔBAP and CP = BP.
O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.
