Question
In the figure given below, CT = TR and AT = A'T. Is CA∥A′R ? If yes, give a proof for the same. [3 MARKS]
Answer:
:
Application of theorem: 1 Mark
Steps: 2Marks
In ΔCATandΔRA′T
CT=RT [Given]
∠CTA=∠RTA′ [Vertically Opposite Angles]
AT=A′T [Given]
∴ΔCAT≅ΔRA′T [By SAS congruence rule]
⇒∠CAT=∠RA′T [Corresponding parts of congruent triangles]
But ∠CATand∠RA′T are alternate interior angles.
If the pair of alternate interior angles is equal then the lines are parallel.
⇒CA∥A′R.
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:
Application of theorem: 1 Mark
Steps: 2Marks
In ΔCATandΔRA′T
CT=RT [Given]
∠CTA=∠RTA′ [Vertically Opposite Angles]
AT=A′T [Given]
∴ΔCAT≅ΔRA′T [By SAS congruence rule]
⇒∠CAT=∠RA′T [Corresponding parts of congruent triangles]
But ∠CATand∠RA′T are alternate interior angles.
If the pair of alternate interior angles is equal then the lines are parallel.
⇒CA∥A′R.
Was this answer helpful ?
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