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ABC is an isosceles triangle with A B =...

ABC is an isosceles triangle with `A B =\ A C`. Draw `A P_|_B C` to show that `/_B =/_C.`

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To solve the problem, we need to show that in triangle ABC, where AB = AC (making it isosceles), the angles at B and C are equal. We will achieve this by constructing a perpendicular from A to BC, denoted as AP, and then proving that triangles ABP and ACP are congruent. ### Step-by-Step Solution: 1. **Draw Triangle ABC**: Start by drawing triangle ABC such that AB = AC. Label the points accordingly. 2. **Draw Perpendicular AP**: From point A, draw a perpendicular line to line segment BC, meeting BC at point P. This means that AP is perpendicular to BC. ...
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Knowledge Check

  • If A(3,4) and B(-5,-2) are the extremities of the base of an isosceles triangle ABC with tan C = 2 , then point C can be

    A
    `((3sqrt(5)-1)/(2),-(1+2sqrt(5)))`
    B
    `(-((3sqrt(5)+5))/(2),3+2sqrt(5))`
    C
    `((3sqrt(5)-1)/(2),3-2sqrt(5))`
    D
    `(-((3sqrt(5)-5))/(2),-(1-2sqrt(5)))`

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    In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

    ABC is an isosceles triangle in which A B" "=""A C . AD bisects exterior angle PAC and C D" "||""A B . Show that (i) /_D A C" "=/_B C A and (ii) ABCD is a parallelogram.

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