Homeschool Math Blog

This is a set of three geometry videos dealing with angles. First, showing that vertical angles are equal: Next, finding out about the angles in a parallelogram . I start out with two parallel lines and a transversal (line that intersects them both). We explore the angles formed, which some of them are corresponding angles, some are vertical angles. I draw a new line, and get a parallelogram. Lastly, here is a short and easy proof about the angles in a triangle .

These are answers to my earlier pos t where I asked if certain figures necessarily are parallelograms. The question was: Does the given information in each diagram guarantee that each is a parallelogram? Figure 1: This one you can't get around; it ends up being a parallelogram, actually a dandy rhombus. Let's prove it. You can notice it has lots of sides of the same length. If we draw a diagonal, we get two triangles with all kinds of same sides: The two triangles ABD and BCD end up having all three sides the same. So by the SSS triangle congruence theorem, they are congruent triangles. Hence, their corresponding angles are the same. I've marked the corresponding angles with the same colors. Actually the triangles are even isosceles so the blue and purple angles are even congruent... but we don't need that fact. To prove ABCD is a parallelogram, we need to prove its two sides are parallel. And for that, it's often handy to use the corresponding angle theorem: if c...

Continuing with the idea in my post about Squares that aren't squares? , let's look at the following "parallelograms". The question is the same: Does the given information in each diagram guarantee that each is a parallelogram? If you don't think so, your mission is to draw a quadrilateral with the given information but that clearly does NOT look like a parallelogram. Figure 1: Figure 2: Figure 3: Figure 4: Again, these problems let students practice logical reasoning, and also learn about parallelograms, of course. See answers here .