Advertisements
Advertisements
Question
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.
Advertisements
Solution
In ∆PRQ and ∆TRS,
side PR ≅ side RT (given)
side QR ≅ side RS (given)
∠PRQ ≅ ∠SRT (vertically opposite angles)
∴ By the SAS test, ∆PRQ ≅ ∆TRS.
∴ side PQ ≅ side ST,
∠QPR ≅ ∠STR,
∠PQR ≅ ∠TSR.
RELATED QUESTIONS
Complete the congruence statement:
ΔBCA ≅?
ΔQRS ≅?
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
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
ΔLMN ≅ ΔPTR
In the following figure, OA = OC and AB = BC.
Prove that: AD = CD
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.
∆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"`
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
