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Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember: Always the same distance apart and never touching. The red line is parallel to the blue line in each of these examples: Parallel lines also point in the same direction. Parallel lines have so much in common.
- Alternate Interior Angles
To help you remember: the angle pairs are on Alternate sides...
- Corresponding Angles
When the two lines being crossed are Parallel Lines the...
- Vertical Angles
Vertical Angles are the angles opposite each other when two...
- Alternate Exterior Angles
To help you remember: the angle pairs are on Alternate sides...
- Line in Geometry
Ray. When it has just one end it is called a "Ray". This is...
- Consecutive Interior Angles
To help you remember: the angle pairs are Consecutive (they...
- Congruent Angles
Congruent Angles Congruent Angles have the same angle (in...
- Parallel Lines Definition
Lines on a plane that never meet. They are always the same...
- Alternate Interior Angles
- Vertical Angles Theorem
- Corresponding Angles Theorem
- Alternate Angles Theorem
- Congruent Supplements Theorem
- Congruent Complements Theorem
- Construction of Two Congruent Angles
- Construction of A Congruent Angle to The Given Angle
According to the vertical angles theorem, vertical angles are always congruent. Let us check the proof of it. Statement: Vertical anglesare congruent. Proof: The proof is simple and is based on straight angles. We already know that angles on a straight lineadd up to 180°. So in the above figure: Conclusion:Vertically opposite angles are always cong...
The corresponding anglesdefinition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other. When a transversal intersects two parallel lines, corresponding angles are always congruent to each other. In this figure,...
When a transversal intersects two parallel lines, each pair of alternate anglesare congruent. Refer to the figure above. We have: ∠1 = ∠5 (corresponding angles) ∠3 = ∠5 (vertically opposite angles) Thus, ∠1 = ∠3 Similarly, we can prove the other three pairs of alternate congruent angles too.
Supplementary angles are those whose sum is 180°. This theorem states that angles supplement to the same angle are congruent angles, whether they are adjacent anglesor not. We can prove this theorem by using the linear pair property of angles, as, ∠1+∠2 = 180° (Linear pair of angles) ∠2+∠3 = 180° (Linear pair of angles) From the above two equations...
Complementary anglesare those whose sum is 90°. This theorem states that angles that complement the same angle are congruent angles, whether they are adjacent angles or not. Let us understand it with the help of the image given below. We can easily prove this theorem as both the angles formed are right angles. ∠a+∠b = 90° (∵∠a and ∠b form 90° angle...
Let's learn the construction of two congruent angles step-wise. Step 1-Draw two horizontal lines of any suitable length with the help of a pencil and a ruler or a straightedge. Step 2- Take any arc on your compass, less than the length of the lines drawn in the first step, and keep the compass tip at the endpoint of the line. Draw the arc keeping t...
By now, you have learned about how to construct two congruent angles in geometry with any measurement. But what if any one angle is given and we have to construct an angle congruent to that? Let's learn it step-wise. Suppose an angle ∠ABC is given to us and we have to create a congruent angle to ∠ABC. Step 1 -Draw a horizontal line of any suitable ...
Mar 26, 2016 · Proving that angles are congruent: If a transversal intersects two parallel lines, then the following angles are congruent (refer to the above figure): Alternate interior angles: The pair of angles 3 and 6 (as well as 4 and 5) are alternate interior angles.
If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. To show that congruent exterior angles will also prove the lines parallel, we will establish a connection between the exterior angles and angles 1 and 2, which are inside the triangles.
Sep 5, 2021 · If two lines are parallel then the interior angles on the same side of the transversal are supplementary (they add uP to \(180^{\circ}\)). If the interior angles of two lines on the same side of the transversal are supplementary then the lines must be parallel.
Prepare a worksheet with several math problems on how to prove lines are parallel. For instance, students are asked to prove the converse of the alternate exterior angles theorem using the two-column proof method. Include a drawing and which angles are congruent. Divide students into pairs.
If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. Visit BYJU'S to learn the properties of parallel lines.
