A parallelogram is a quadrilateral whose opposite sides are parallel. In the figure below, is a parallelogram. is parallel to and is parallel to .
In this post, aside from being parallel, we will also prove that the opposite sides of a parallelogram are congruent.
A secant is a line that intersects a circle at two points. In the figure below, is formed by two secants. The angle intercepts two arcs and . In this post, we will prove that the measure of the angle formed by two secants intersecting outside a circle is half the difference of the arcs intercepted by it.
To prove this theorem we will connect and use the Inscribed Angle Theorem and Exterior Angle Theorem.
Angle Secant Theorem
The angle measure formed by two secants intersecting outside a circle is half the difference of the arcs intercepted by it Continue reading
It’s Friday and as I have mentioned in the previous post, I will be posting proof problems that are accessible to advanced high school students every Friday. Here is the Mathematics Proof Problem of the Week.
If , and , prove that
The proof of this problem and the second Math Proof of the Week will be posted next Friday.
Again, the problems in this series are intended for advanced high school math students. If the proof is too easy for you, no need to answer it.