1/22/2024 0 Comments Proofs using cpctcNow verify that AC ≅ CK and all the interior angles are congruent:ĪC ≅ CK (the altitude of the base of an isosceles triangle bisects the base, since it is by definition the perpendicular bisector) So, we have one leg and a hypotenuse of △JAC congruent to the corresponding leg and hypotenuse of △JCK. We know by the reflexive property that side JC ≅ JC (it is used in both triangles), and we know that the two hypotenuses, which began our proof as equal-length legs of an isosceles triangle, are congruent. We have two right triangles, △JAC and △JCK, sharing side JC. We have two right angles at Point C, ∠JCA and ∠JCK. That altitude, JC, complies with the Isosceles Triangle Theorem, which makes the perpendicular bisector of the base the angle bisector of the vertex angle. Recall that the altitude of a triangle is a line perpendicular to the base, passing through the opposite angle. Can you guess how?Ĭonstruct an altitude from side AK. We are about to turn those legs into hypotenuses of two right triangles. We know by definition that JA ≅ JK, because they are legs. To prove that two right triangles are congruent if their corresponding hypotenuses and one leg are congruent, we start with an isosceles triangle. Once proven, it can be used as much as you need. We have to enlist the aid of a different type of triangle. So we have to be very mathematically clever. Of course you can't, because the hypotenuse of a right triangle is always (always!) opposite the right angle. Hold on, you say, that so-called theorem only spoke about two legs, and didn't even mention an angle?Īha, have you forgotten about our given right angle? Every right triangle has one, and if we can somehow manage to squeeze that right angle between the hypotenuse and another leg.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |