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
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 triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
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
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.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
Which of the following rule is not sufficient to verify the congruency of two triangles
The congruent figures super impose each other completely.
Two figures are congruent, if they have the same shape.
