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### Course: High school geometry>Unit 3

Lesson 1: Transformations & congruence

Finding missing triangle angle measures and identifying parallel lines from angle measures on transversals help prepare us to learn about congruence.
Let’s refresh some concepts that will come in handy as you start the congruence unit of the high school geometry course. You’ll see a summary of each concept, along with a sample item, links for more practice, and some info about why you will need the concept for the unit ahead.
This article only includes concepts from earlier courses. There are also concepts within this high school geometry course that are important to understanding congruence. If you have not yet mastered the Intro to Euclidean geometry lesson, the Rigid transformations overview lesson, or the Properties & definitions of transformations lesson, it may be helpful for you to review those before going farther into the unit ahead.

## Using angle relationships

### What is this, and why do we need it?

When lines intersect, especially when a transversal intersects a pair of parallel lines, the intersections form angles with special relationships. We will use these angle relationships to explain how to construct parallel or perpendicular lines, which in turn help us to bisect angles and line segments. We will also use parallel sides to reveal more properties of parallelograms.

### Practice

Problem 1
Exactly two of the lines in the following figure are parallel.
The figure is not to scale.
Which two lines are parallel?

For more practice, go to Angle relationships with parallel lines.

### Where will we use this?

Here are a few of the exercises where reviewing angle relationships might be helpful:

## Finding missing angle measures in triangles

### What is this, and why do we need it?

The three angle measures in any triangle add up to $180\mathrm{°}$. We'll use congruence along with other concepts, like the fact that the interior angle measures of a triangle sum to $180\mathrm{°}$, to find missing measurements.

### Practice

Problem 2
Find the value of $x$ in the triangle shown below.
$x=$
$\mathrm{°}$

For more practice, go to Find angles in triangles.

### Where will we use this?

Here are the first few exercises where reviewing angle measures in triangles might be helpful.

## Want to join the conversation?

• For the first practice question,how do we know that line a and line d have alternate interior angles and corresponding angles,and why does it not work for line b and line c?
• Any pair of lines have these angles, so the question is are they congruent (if you use alternate interior or alternate exterior or corresponding)?
or are they supplementary (if you use same side interior or same side exterior)?
For any one line and the transversal, you can use the fact that adjacent angle are supplementary and vertical angles are congruent.
Thus, for b and c, alternate interior angles would be 88 degrees (180-92) and 91 degrees which are not congruent, thus not parallel. For corresponding angles, you would get the same results of 88 and 91 degrees which are not congruent.
• what exactly does congruence mean?
• congruence is to figures as equal is to expressions. If two things are congruent, they are the same size and/or the same shape.
• As a freshman who started high school yesterday, I am really going to need this as I am in an honors course
• same bro
• How do you know which one is parallel and which one is not?
(1 vote)
• If you fine two congruent angles, you know it is parallel. Also, you can use a compass. If you're still confused, the next few videos shall help.

-Duskpin the Avatar
• I am still confused as to how a and d were parallel. line d was 89 degrees and line a was 91.
• the angles add up to 180 degrees and so it makes them parallel. hope that helps.
• i am a little confused here. what is congruence exactly??
• Congruence compares two line segments, shapes, or 2-d figures. It two things are exactly the same shape and same size, then they are congruent. If two line segments are congruent, that would mean their lengths would be the same. If two figures are congruent (like congruent triangles), then their angles are the same and their side lengths are the same.
• I don't get this. could i get help?
• Congruence means that the shapes are equal in all ways which also means that with a set of rigid transformations you can map one onto the other.
• Why was problem 1 answers parallel ?
• We have no name for two angles that are alternate (opposite side of transversal) with one interior and one exterior angles. Since angles which form a line are supplementary, we could subtract 180-91=89 to get the angle right above 91 on line a, then use alternate exterior angles congruent for parallel lines. We could also do the same for the 89 degree angle which would give the angle to the right as 91 degress, and use corresponding angles congruent, thus lines are parallel.
• I have a hard time doing geometry. do you have any tips on how to get better?
• How do you know which one is parallel and which one is not?