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प्रश्न
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.
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उत्तर
The triangles are congruent by the SAS Test under the correspondance XWZ ↔ YWZ.
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.
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
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 ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...[Vertically opposite angles]
∴ ΔPTQ ≅ ΔSTR ...`square` test
∴ `{:("∠TPQ" ≅ square),("and" square ≅ "∠TRS"):}}` ...corresponding angles of congruent triangles
seg PQ ≅ `square` ...corresponding sides of congruent triangles
In the following diagram, ABCD is a square and APB is an equilateral triangle.
(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.
State, whether the pairs of triangles given in the following figures are congruent or not:
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P, Q, R to I are equal.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
