....'shall be equal, that is, the triangle will be either isosceles or equilateral. PROPOSITION IX. THEOREM. The angles opposite the equal sides of an isosceles triangle are equal. Let the sides AB, AC, of the triangle ABC be equal, then will the angle C be equal to the angle B....

...triangles ABC and DEF, having Angle A = D, angle B = E and AB=DE, then will AC=DF, CB=FE and angle C=F. 3. The angles opposite the equal sides of an isosceles triangle are equal. Thus, if ABC be an isosceles triangle, the angle A = B. D B 4. A line drawn from the vertical angle,...

...: thus, the equal angles D and A, lie opposite the equal sides EF and BC. PROPOSITION XIV. THEOREM. The angles opposite the equal sides of an isosceles triangle are equal. Let the sides AB, AC, of the triangle ABC be equal, then will the angle C be equal to the angle B....

...(IIypoth.) : hence ZA = D. In the same manner, it may be proved that ZB = E, and ZC = F. XXV. Theorem. The angles opposite the equal sides of an isosceles triangle are equal. HYPOTH. AB = AC. To BE PROVED. ZB = C. PROOF. Bisect Z BAC by the line AD ; then AB = AC (Hypoth.),...

...out of many, as an example, will show what I mean. The class had just proved the proposition, that the angles opposite the equal sides of an isosceles triangle are equal, whereupon I asked, if any could prove that all the angles of an equilateral triangle were equal. After...

...unequal angles of a triangle is greater than the side opposite the less, — having first proved that the angles opposite the equal sides of an isosceles triangle are equal, and that the angle opposite the greater of two unequal sides of a triangle is greater than the angle...

...opposite interior angles. 5. Show that the angles of an equilateral triangle are equal. 6. Show that the angles opposite the equal sides of an isosceles triangle are equal. 7. Show that two triangles are equal if two sides and included angle of one triangle are equal to the...

...point of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. 3. The angles opposite the equal sides of an isosceles triangle are equal. 4. If two angles of a triangle are equal, the sides opposite the equal angles are equal and the triangle...

...B fall exactly on E ? Conclusion. 33. Problem IV. To bisect a given straight line. THEOREM VIII 34. The angles opposite the equal sides of an isosceles triangle are equal. Hyp. Let AB and AC be the equal sides of the isos. A ABC. To prove that ZB = Z O. Sue. 1. Draw a line...

...combination he has and whether or not it is sufficient for his purpose. For instance, in the proposition, "The angles opposite the equal sides of an isosceles triangle are equal," the two legs might be colored blue, the construction line bisecting the vertex angle yellow, and the halves...