Engineering students at Lancaster College last year received an average of $6,400 in scholarships and grants. This year, the ave
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The altitudes of equal length, BE and CF gives AB = AC, from which we have;
- ∆ABC is an isosceles triangle
From the given description, we have;
BE = CF
<CFB = <BEC = 90° All right angles are congruent
BC = BC by reflexive property of congruency
BC = The hypotenuse side of triangles ∆BFC and ∆CEB
Therefore;
∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.
Therefore;
BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Similarly, we have;
∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency
Which gives;
FA = AE by CPCTC
BF + FA = CE + AE, by substitution property of equality
BF + FA = AB
CE + AE = AC
Therefore;
- AB = AC
Therefore;
- ∆ABC is an isosceles triangle
Learn more about rules of congruency here:
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Answer:
<h2>A = 20</h2><h2>P = 6√10</h2>Step-by-step explanation:
The formula of a distance between two points:
A(-3, 0) , B(3, 2)
A(-3, 0), D(-2, -3)
AB = CD and AD = BC
The area of a rectangle:
Substitute:
The perimeter of a rectangle:
Substitute: