Advertisements
Advertisements
Question
Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.
Advertisements
Solution
In ΔABC and ΔPQR
BC = QR
AD and PM are medians of BC and QR respectively
⇒ BD = DC = QM = MR
In ΔABD and ΔPQM
AB = PQ
D = PM
BD = QM
Therefore, ΔABD ≅ ΔPQMABD PQM ...(SSS criteria)
Hence, ∠B = ∠Q
Now in ΔABC and ΔPQR
AB = PQ
BC = QR
∠B = ∠Q
Therefore, ΔABC ≅ ΔPQRABC PQR. ...(SAS criteria)
APPEARS IN
RELATED QUESTIONS
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the othe Prove that the triangles are congruent.
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
State, whether the pairs of triangles given in the following figures are congruent or not:
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
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°).
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.
PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.
If AB = QR, BC = PR and CA = PQ, then ______.
