Advertisements
Advertisements
Question
In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC.
Advertisements
Solution
Given that, the sides BA and CA have been produced such that BA =AD and CA= AE and
given to prove DE || BC
Consider triangle BAC and , DAE
We have
BA = ADand CA = AE [∵ given in the data]
And also ∠BAC=∠DAE [ ∵vertically opposite
angles]
So, by SAS congruence criterion, we have ΔBAC ≅ ΔDAE
⇒ BC = DE and ∠DEA=∠BCA, ∠EDA ∠CBA
[Corresponding parts of congruent triangles are equal]
Now, DE and BC are two lines intersected by a transversal DB such that ∠DEA =∠BCA,
i.e., alternate angles are equal
Therefore, DE || BC
APPEARS IN
RELATED QUESTIONS
Complete the congruence statement:
ΔBCA ≅?
ΔQRS ≅?
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.
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.
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.
If the following pair of the triangle is congruent? state the condition of congruency :
In ΔABC and ΔDEF, ∠B = ∠E = 90o; AC = DF and BC = EF.
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
In the figure, AB = EF, BC = DE, AB and FE are perpendiculars on BE. Prove that ΔABD ≅ ΔFEC
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆YZX ≅ ∆PQR
