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Q: Which sets are equal (abc) (bca) (abd)?
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What is the best course BBA or BCA?

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How do you prove the diagonals of a rhombus divide the rhombus into four congruent triangles?

Take a rhombus ABCD. A rhombus as 4 equal sides, thus AB = BC = CD = DA Draw in 1 diagonal AC. This splits the rhombus into 2 triangles. ABC and CDA with side AB = CD, BC = DA and AC common to both triangles. Thus ABC and CDA are congruent by Side-Side-Side. Triangles ABC and CDA are isosceles triangles since they have two equal sides (AB = BC and CD = DA) thus angles DAC = DCA = BAC = BCA. Specifically DAC = BAC. But DAC + BAC = DAB, thus DAC = BAC = ½ DAB; similarly DCA = BCA = ½ BCD = ½ DAB Drawing in the other diagonal BD, the same arguments show triangles ABD and CDB are congruent and angles ADB = CDB = ABD = CBD = ½ ABC Let the point where the diagonals meet be E. We now have 4 triangles ABE, BCE, CDE and DAE with equivalent angles and sides: Angles DAE* = BAE = BCE = DCE (= ½ DAB) Angles ABE = CBE = CDE = ADE (= ½ ABD) Sides AB = BC = CD = DA Thus the 4 triangles are congruent by Angle-Angle-Side. *Angle DAE = DAC since E lines along AC; similarly for all the other angles involving point E, ie angle BCE = BCA, ADB = ADE, etc


What is the mathematical reason for why the angels in a triangle add upp to 180?

First draw a triangle with vertices A, B, and C. Let's let C be at the top and B and A the base of the triangle. A' and B' are on the line drawn parallel to the base and through point vertex C. Place A' on the right of C and B' on the left of C. Of course it works for any triangle, but I am trying to make the picture easy so then you can generalize.if ABC is a triangle then


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In a circle chord AC has a length of 6 If the length of arc ABC is equal to one-sixth of the circumference of the circle what is the area of the circle?

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