Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
3. Proving Triangle Congruence by SAS
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Exercise 23 Page 250

To use the SAS Congruence Theorem you have to copy a side, then an angle, and finally another side.

Practice makes perfect

To copy the triangle using the SAS Congruence Theorem, we have to copy two sides and its included angle. Let's start by copying the base of the triangle AC. To do that, we will begin by drawing a straight line directly underneath △ ABC. Make sure it's longer than AC.

Now we have to copy the length of AC using a compass. Having measured the length of AC, we will use the same setting to measure that exact distance on our segment. Note that we will erase whatever is leftover.

Next, we are going to have to copy either ∠ A or ∠ C from △ ABC. How about we copy ∠ A and make ∠ D the same size. To do that, we draw an arc around D like below.

Keeping the compass settings intact, we measure the angle on the original and copy it so that ∠ A ≅ ∠ D. Knowing the direction DE should be drawn, we go ahead and draw that's going to be our second congruent side. Make it a long line!

Now we just have to measure the distance of AB and limit the line we just drew above to that same distance. We will erase what's left over.

Finally, we will connect the endpoint of E and F and we have made our copy.