Line p is parallel to line q. Which proof explains why the sun of the interior angles of the triangle must be 180
1 answer:
Answer:
We consider a triangle ABC as attached in the answer.
We draw a line parallel to AB that passes through point C.
Angles C and C' are vertical angles, therefore ∠C = ∠C'.
Angles B and B' are corresponding angles, therefore ∠B = ∠B'.
Angles A and A' are corresponding angles, therefore ∠A = ∠A'.
it can be seen that angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.
The three angles A', B', and C' form together a straight angle so, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.
This proofs that sum of angles of a triangle is equal to 180.
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Answer:
Length of side of rhombus is
Step-by-step explanation:
Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.
It is also given that AB=a and AC=b
Let side of rhombus is x.
In ΔCEF and ΔCBA
∠CEF=∠CBA (∵Corresponding angles)
∠CFE=∠CAB (∵Corresponding angles)
By AA similarity rule, ΔCEF~ΔCBA
∴ their sides are in proportion
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Hence, length of side of rhombus is
