On number 5, I have been able to prove the => for all three of them, but I am struggling with the <= for (i) and (ii). Any hints on where to start?-Lauren
Lauren, for (i)<= use the fact that altitudes are perpendicular so we have right triangles. They have an equal leg (the base of the big triangle) and the hypotenuse of both are equal (given-they are the two altitudes). Now use Theorem 9 to prove conguent triangles and then the base angles of the big triangle are equal-then use theorem 5. Hope this helps. ~Janelle
Lauren, I am having trouble with the <= for (iii) could you help me out there? ~Janelle
for #5, 3iii <=, DE and AB are parallel since they are medians. So big triangle and inner triangle are similar. so 2 bottom angles are equal so is an iso triangle. - Sue
for ii <=, can we do theorem 21? we know some equal angles. This would make for some equal sides if the sines are equal and than work around that? - Sue
Sue, since we only have to do two of the three, you might want to do i and iii. These proofs are much easier. -Jennie
Does anyone have hints for #3,4, or 7?
For #4, try looking for different instances of Menalaus' theorem inside the triangle and combine them. -Tim
Does anyone have a hint for 3? - Dana
For 7, use Thm 16 to makes two different sets of lines parallel. -Mary
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