math portfolio @rnathematix - Tumblr Blog

Pi explained visually.

pi is one of those very simple concepts that is never explained simply

Theorems on Secants, Tangents and Chords

→ Theorems on Line Segments

Chord-Chord Theorem: If two chords intersect in a circle, then the product of the lengths of the segments on one chord is equal to the product of the lengths of the segments on the other.

Secant-Secant Theorem: If two secants are drawn to a circle from an exterior point, the product of the lengths of one secant and its external secant segment is equal to the product of the lengths of the other secant and its external secant segment.

Tangent-Secant Theorem: If a tangent and a secant are drawn to a circle from an exterior point of the circle, the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external secant segment.

→ Theorems on Angles

Interior Secant-Secant Angle Theorem: The measure of an angle formed by two secants which intersect in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Exterior Secant-Secant Angle Theorem: The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.

Exterior Secant-Tangent Angle Theorem: The measure of an angle formed by a secant and a tangent that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.

Tangent-Tangent Angle Theorem: The measure of an angle formed by two intersecting tangents is one-half the difference of the measures of the intercepted arcs.

#lesson #sec tan cho

berriescitrusavocado-blog

rnathematix

We can use the concepts of central angles and arcs when we slice cake into equal parts. When there are guests around, or if you’re alone and just want to distribute your fill of cake over the week, you’d have to usually distribute the cake into equal parts. We’d start slicing from the middle, and you’ll see that it looks like a central angle!

#application #cangles-arcs

Central Angles and Arcs

Chord-Central Angles Conjecture: If two chords in a circle are congruent, then they determine two central angles that are congruent.

Chord-Arcs Conjecture: If two chords in a circle are congruent, then their intercepted arcs are congruent.

Perpendicular to a Chord Conjecture: The perpendicular from the center of a circle to a chord is the bisector of the chord.

Chord Distance to Center Conjecture: Two congruent chords in a circle are equidistant from the center of the circle.

Perpendicular Bisector of a Chord Conjecture: The perpendicular bisector of a chord passes through the center of a circle.

#lesson #cangles-arcs

Knowing the parts of a circle are beneficial by itself because it broadens our vocabulary and helps us express out thoughts better, and more specifically!

#application #circle parts

Parts of a Circle

Chord: A line segment whose two endpoints lie on the circle.

Radius: A line segment which starts at the center of the circle and ends on any point on the circle.

Diameter: A chord that equally halves the circle into two parts.

Secant: A line segment that passes the circle twice.

Tangent: A line segment that passes the circle only once.

Central Angle: An angle whose vertex is the circle ‘s center.

Inscribed Angle: An angle formed by two chords which have the same endpoint.

Arc: The distance of one point on the circumference of the circle to another.

#Intercepted Arc: The part of the circumference that lies between two

lines that interest it.

#Major Arc: The longer arc when a chord/secant passes through a circle.

#Minor Arc: The major arc’s counterpart, it is the shorter arc.

Concentric Circles (not shown): A smaller circle within a circle.

#lesson #circle parts

My love is a spiral, not a circle. A circle goes around, but never goes anywhere, while a spiral goes around, but constantly rises.

Jarod Kintz, My Love Can Only Occupy One Person at a Time

#quote

Special Right Triangles Practice

Caine was outside drawing a still life scene of his city’s lamp posts glowing at night. He was sketching and realized it was already very late at night that he’d have to go home! He had to leave quickly or else he’d miss his ride home, so he had to write down the measurements of the lamp posts in his drawing. He concluded that the hypotenuse, he says as he remembers his math lessons, of the lamp post to the ground was about 2 inches on his drawing pad. The height of the post and length of its shadow were more or less the same. What are the measures of these lengths?

#practice #special triangles

Special triangles follow a certain pattern. Similarly, nature does too! There is this phenomenon called the Golden Ratio that can be seen in nature, art and architecture to name a few.

#application #special triangles

Special Right Triangles

There are certain triangles that have a shortcut to finding the measures of its sides! These are called Special Right Triangles. These triangles are namely the 30-60-90 triangle and the 45-45-90. As you can see, their names are based on the angles they have! Watch the video to learn more about it!

#lesson #special triangles

Pythagorean Theorem Practice

The local barangay council was planning a park. They had thought of making a slide 6 feet tall and 8 feet long. With dimensions such as those, how long should the slide be to maintain balance for the overall structure?

#practice #pythagorean theorem

Imagine yourself cycling on the side walk and your house is just a few meters ahead, right across you. Would you cross diagonally cutting corners to arrive there or continue cycling and following the designated path?

When thinking about this, we use the concept of the Pythagorean Theorem!

#application #pythagorean theorem

Pythagorean Theorem

The Pythagorean theorem was made by Pythagoras nearly 2000 years ago, and is essentially this one equation: a²+ b² = c²

The a is the triangle’s shorter leg, b is the longer leg and c is the hypotenuse of the triangle. It was discovered that when the squares of a and b combined would be the square of c !

#lesson #pythagorean theorem

Right Triangle Similarity Theorem Practice

Anna is making kirigami, a variant of origami except with cutting. She cut a triangle with the sides 3, 4 and 5. The instructions require her to cut up a triangle four times the size of the triangle she just cut. She cut out a triangle with the dimensions 12, 16 and 20. Were her calculations correct?

Check under the cut to find out the answer!

#practice #triangle similarity

Right Triangle Similarity Theorems

We have three similarity theorems for triangles, which are SAS, SSS and the AA postulate.

What’s the difference of a postulate and a theorem?

Postulate // It’s a statement that’s already true, no proof needed.

Theorem // It’s a statement that’s true when proven.

AA Postulate

AA stands for Angle-Angle. This is a postulate, so once you see that two triangles have two congruent angles like the name suggests, then they’re automatically proportional! It’s as simple as that.

SAS Theorem

SAS stands for Side-Angle-Side. It’s a theorem, so there’ll be a little bit of computation involved to prove it. We’ll be proving if the two triangles are proportionate when the ratio of two corresponding sides with an angle in between are the same.

SSS Theorem

SSS stands for Side-Side-Side. It’s a theorem like SAS, but what we have to prove would be if two triangles have proportionate sides. We’ll need to check if their corresponding sides or perimeter have the same ratios.

#lesson #triangle similarity

cyantifical

Math gives you every reason to hope that to every problem, there is a solution.

Anonymous (via cyantifical)

#quote

Trending Blogs

Recently Viewed Blogs

math portfolio