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Answer:
- You have to fill the blank squares to complete the table.
- See the figure attached and the explantion below.
Explanation:
The figure attached shows the three squares that you have to fill to complete the table to summarize the different <em>theorems</em> to <em>prove triangles are congruent.</em>
<u>1. SAS</u>
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SAS stands for Side Angle Side. That means that whenever two sides and the included angle on one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.
Thick marks are used to mark the corrsponding parts, sides or angles that are congruent. That is why the two triangles to the first triangles on the image (on the upper square to the right) are marked:
- One thick straight mark for two sides that are congruent
- Two thick straight marks for the other two sides that are congruent
- On thick curved mark for the two angles that are congruent
In that way, the figures show two triangles, with two congruent sides and the included angle congruent, to prove that the two triangles are congruent by the SAS theorem.
<u>2. ASA</u>
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ASA stands for Angle Side Angle.
The ASA congruency theorem states that if two angles of a triangle and the included side are congruent, then the two triangles are congruent.
Thus you have to add the legend "Two congruent angles with and included side", which means that if the two angles and the included side on one triangle are congruent to two angles and the included side of other triangles, then both triangles are congruent.
The rule to mark the sides and angles that are congruent is with the use of thick marks. This is how it was done in the drawing of the two triangles in the lower right square:
- One thick straight mark for two sides that are congruent
- One thick curved mark for two angles that are congruent
- Two thick curved marks for the other two angles that are congruent
