Isosceles Triangles for Dummies

Isosceles triangle

As our researchers wander about the internet wondering about the internet, they sometimes come across an answer to a question and realize that neither the question nor the answer makes any sense. They usually file those in the folder called "ask a stupid question, get a stupid answer." The folks at eHow.com are some of the worst offenders, since many of them simply churn out content based on search terms harvested by a Demand Media bot, so sometimes the "contributor" must decide what the question even means before answering it. That can be a recipe for disaster, much as it was the day Sarah Celebi tried to explain "How to Use the Pythagorean Theorem for Isosceles Triangles" (moved to Sciencing.com by the folks at Leaf Group)

We have to admit that we really aren't certain what the OQ wanted to know, but Sarah decided that the questioner wanted to know how to determine the length of the two equal sides of an isosceles triangle of known base and height. Or at least we think that's what she figured. Celebi started out with a sensible statement...

"By drawing a straight line down the center of an isosceles triangle, it can be divided into two congruent right triangles, and the Pythagorean theorem can easily be used to solve for the length of an unknown side"...

...and moved on. Unfortunately, things deteriorated as the post dragged on. Sarah's process for solving this problem is long and torturous, involving drawing the triangle to scale and in a specific orientation. She then instructs her reader to "Draw a straight line down the middle of the triangle from the vertex to the base." Since the question was probably submitted by a geometry student, it might have been easier to say "construct a perpendicular bisector," but Sarah's content editor would probably have called that "jargon" since no one takes geometry (or any math, for that matter) in J-school. In any case, Celebi wants her reader to

3. Write the values of the lengths of the known sides of the triangle next to the sides they match. These values may come from a specific math problem or from measurements for a certain project. Write "3 in." next to the line drawn in Step 2 and "4 in." on either side of this line at the base of the triangle.
4. Determine which side is of unknown length and use the Pythagorean theorem to solve for it using a calculator. The unknown side is the hypotenuse of each of the two triangles.
5. Label the hypotenuse "C" and either of the legs of the triangle "A" and the other one "B."

Now, we figured that was an awful lot of drawing and labeling to identify the sides of a triangle, not to mention that steps 4 and 5 are reversed. ¡No bueno, Sarah! ¡No bueno! Celebi next, rather wordily, instructs her readers in the use of the Pythagorean Theorem to determine the length of the two identical sides. She did, in fact, get the right answer -- but talk about going the long way 'round! All this rubbish about drawing the picture and labeling the sides is utter bull, inserted in part because neither Celebi nor the content editor could visualize the triangle in question and perhaps in part to reach the minimum word count...

Buried in the "Tips" section of the post is the main reason our researcher flagged Celebi's post as a Dumbass of the Day candidate. That's where she defines the hypotenuse as "the line that connects the base and height of a right triangle." Dumbass, indeed...

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