Download Congruent polygons - Moore Public Schools

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SECTION 4.2
Congruent Figures ­ have the same size and shape. When two figures are congruent you can move them flip them or turn them and they will still be congruent. They are like puzzle pieces. When you have a piece that fits into the puzzle, you may have to flip it, or turn it, so that you can fit it in as long as it is congruent to the space that you are putting it.
Congruent Polygons ­ are congruent figures that have congruent corresponding parts which are their matching side and angles, and matching vertices and corresponding vertices. *When you name congruent polygons, always list corresponding vertices in the same order.
Notice that these two figures are congruent but they are back to back. Their corresponding parts are:
The last part is a congruent statement. It names the polygons by putting corresponding parts together.
You may not have a picture when having to list congruent corresponding parts you may just have a congruent statement.
Congruent Statement: *A congruent statement tells you everything you need to know because order matters. We must write congruent statements by their corresponding congruent parts so that we know which parts are congruent. By using the congruent statement we can state which angles, sides and vertices are congruent (need to name the angles using 3 letters).
Angles:
Sides:
Vertices:
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take the triangle, copy, paste and rotate rename angles
Congurent Figures have congruent corresponding parts.
Congruent polygons have congruent corresponding sides and angles.
List all pairs of corresponding parts:
1) Corresponding angles:
2) Corresponding sides:
Congruent statement:
copy, rotate
List all pairs of corresponding parts:
1) Corresponding angles:
2) Corresponding sides:
Congruent statement:
Definition of congruent figures: If all corresponding parts of 2 figures are congruent then the two figures are congruent. 3
By knowing two polygons are congruent you can find missing angles or use angles from one figure to help fill in missing angles in another figure.
Example: When deciding whether polygons are congruent, each part must have a corresponding congruent part or the two figures are not congruent.
Example: Decide whether the the triangles are congruent and justify your answer. If yes, write a congruence statement.
*Ask yourself first
how many pairs should I have congruent and
make sure you have
that many in the end.
Another example: Can you conclude that Justify your answer.
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When stating reasons on a proof where you are trying to prove triangles congruent, if you can prove all corresponding parts are congruent (and using theorem 4.3 may help prove a third angle congruent), then you have proven the triangles congruent by the Definition of Congruent triangles!
Given: Prove:
Statements
Reasons
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