# Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.

### Popular Tutorials in Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.

#### What is Inductive Reasoning?

You probably observe data and patterns to make predictions or conjectures on a regular basis. If so, you are using inductive reasoning. Check out the video to learn more!

#### How Do You Construct a Line Parallel to Another Line Through a Given Point?

A compass is a very handy tool! In this tutorial, you'll see how to use a compass and straightedge to construct parallel lines!

#### What is the Corresponding Angles Postulate?

When a transversal intersects parallel lines, the corresponding angles created have a special relationship. The corresponding angles postulate looks at that relationship! Follow along with this tutorial to learn about this postulate.

#### What is the Converse of the Corresponding Angles Postulate?

The corresponding angles postulate states that when a transversal intersects parallel lines, the corresponding angles are congruent. What if you go the other way and start with corresponding angles that are congruent? Is the converse of this postulate true? This tutorial explores exactly that!

#### How Do You Determine if Triangles on the Coordinate Plane are Congruent?

There are many ways to show that two triangles are congruent. This tutorial shows you how to use a triangle congruence postulate to show that two triangles on the coordinate plane are congruent to each other!

#### What is the Side-Angle-Side Postulate for Triangle Congruence?

The Side-Angle-Side postulate is just one of many postulates you can use to show two triangles are congruent. This tutorial introduces you to the SAS postulate and shows you how to use it!

#### How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?

If you want to determine if a point is on the perpendicular bisector of a line segment, the Perpendicular Bisector Theorem and its converse might come in handy. This tutorial gives a great example of how to tell if a given point is a perpendicular bisector of a segment!

#### How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?

If you're given 3 side measurements, there's a quick way to determine if those three sides can form a triangle. Follow along with this tutorial and learn what relationship these sides need in order to form a triangle.

#### How Do You Construct a Perpendicular Bisector?

This tutorial shows you how to construct a perpendicular bisector using only a compass and a straightedge!

#### How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?

Trying to figure out which side of a trianlge is the shortest? How about the longest? All you need to get your answer are the angle measurements of the triangle! How does it work? Watch this tutorial to find out!

#### What is the Circumcenter of a Triangle?

This tutorial explains the ins and outs of the circumcenter of a triangle. You'll see how to build up from the Perpendicular Bisector Theorem to find the circumcenter of a triangle.

#### What is the Incenter of a Triangle?

The incenter of a triangle deals with the angle bisectors of a triangle. This tutorial shows you how to find the incenter of a triangle by first finding the angle bisectors.

#### How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?

When you make diagonals inside a rectangle, those diagonals are congruent. With this information, you can find the value of a variable that's part of a measurement of a diagonal. This tutorial shows you the steps.

#### How Do You Use the Triangle Proportionality Theorem to Find Missing Lengths in a Diagram?

This tutorial shows you how the Triangle Proportionality Theorem can be used to find a missing length in a diagram. Take a look!

#### How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?

When you want to know if two chords are the same distance away from the center of the circle, there's a quick way to get the answer. In this tutorial, you'll learn how to find that answer and figure out which chords are equidistant from the center.

#### How Do You Use Intersecting Chords to Find Arc Measures in a Circle?

This tutorial shows you how to use your knowledge of intersecting arcs in a circle to find a missing arc measurement. Take a look!

#### How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?

This tutorial shows you how to use your knowledge of intersecting chords in a circle to find a missing angle measurement.

#### How Do You Find Missing Angles in an Isosceles Triangle?

Trying to find a missing interior angle measurement in a triangle? See if you're working with a special type of triangle such as an equilateral or isosceles triangle. If you are, that knowledge can help you. In this tutorial, see how identifying your triangle first can be very helpful in solving for that missing measurement. Take a look!

#### How Do You Find Missing Angles in a Triangle With Variables?

Looking for the measurements of the interior angles of a given triangle? The Triangle Sum theorem might help. This theorem states that the interior angles of a triangle ALWAYS add up to 180 degrees! This tutorial shows you how to use that information to find those interior angle measurements.

#### How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?

Trying to find a missing interior angle measurement in a triangle? See if you're working with a special type of triangle such as an equilateral or isosceles triangle. If you are, that knowledge can help you. In this tutorial, see how identifying your triangle first can be very helpful in solving for that missing measurement. Take a look!

#### How Do You Find Missing Angles in a Transversal Diagram?

Got a diagram of a transversal intersecting parallel lines? Trying to figure out all the angle measurements? Take a look at this tutorial, and you'll see how find all the missing angle measurements by identifying vertical, corresponding, adjacent, and alternate exterior angles!

#### How Do You Find a Value for x that Makes Two Lines Parallel?

Got a transversal intersecting two lines? Trying to figure out if those lines are parallel? You could test to see if corresponding angles are congruent. This tutorial shows you how!

#### What is a Rectangle?

A rectangle is one of the many fundamental shapes you'll see in math. Rectangles have special properties that can be very useful in helping you solve a problem. This tutorial introduces you to rectangles and explains their interesting qualities!

#### What is a Trapezoid?

A trapezoid is a special type of quadrilateral with some special properties. This tutorial introduces you to trapezoids and gives you a look at the special properties needed for a quadrilateral to be called a trapezoid. Check it out!

#### What are Supplementary Angles?

Knowing about supplementary angles can be very useful in solving for missing angle measurements. This tutorial introduces you to supplementary angles and shows you how to use them to solve for a missing angle measurement. Take a look!

#### What are Vertical Angles?

Vertical angles have a very special quality. They are always congruent to one another! Check out this tutorial to learn about and see how to identify vertical angles!

#### What Does Congruent Mean?

If two figures have the same size and shape, then they are congruent. The term congruent is often used to describe figures like this. In this tutorial, take a look at the term congruent!

#### What are Parallel Lines?

Lines that are parallel have a very special quality. Without this quality, these lines are not parallel. In this tutorial, take a look at parallel lines and see how they are different from any other kind of lines!

#### What are Perpendicular Lines?

Perpendicular lines have a special property. The angles formed by perpendicular lines will always be the same. Check out this tutorial to learn about perpendicular lines and see a cool trick involving these special lines!

#### What are Skew Lines?

Ever heard of skew lines? They're pretty cool! Take a look at this tutorial and you'll be introduced to skew lines.

#### How Do You Find the Sum of the Interior Angles of a Polygon?

Polygons have all kinds of neat properties! For example, if you know the number of sides of a polygon, you can figure out the sum of the interior angles. That knowledge can be very useful when you're solving for a missing interior angle measurement. Check out this tutorial to learn how to find the sum of the interior angles of a polygon!

#### What is the Triangle Sum Theorem?

When you're dealing with triangles, the Triangle Sum theorem can be very useful in finding interior angle measurements. In this tutorial, learn how to find this helpful theorem!