# How to write a congruence statement for triangles

Contact Triangles and Congruence Triangles have 6 parts. Can you guess them? This is very different! The notation convention for congruence subtly includes information about which vertices correspond. To write a correct congruence statement, the implied order must be the correct one.

So once the order is set up properly at the beginning, it is easy to read off all 6 congruences. Congruence Criteria It turns out that knowing some of the six congruences of corresponding sides and angles are enough to guarantee congruence of the triangle and the truth of all six congruences.

So we do not prove it but use it to prove other criteria. If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.

If 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent. This was proved by using SAS to make "copies" of the two triangles side by side so that together they form a kite, including a diagonal. Then using what was proved about kites, diagonal cuts the kite into two congruent triangles.

## Congruence and triangles

Details of this proof are at this link. If two angle in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent. This proof was left to reading and was not presented in class.

Again, one can make congruent copies of each triangle so that the copies share a side. For the proof, see this link. In general there are two sets of congruent triangles with the same SSA data. Examples were investigated in class by a construction experiment.

In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

The proof of this case again starts by making congruent copies of the triangles side by side so that the congruent legs are shared. The resulting figure is an isosceles triangle with altitude, so the two triangles are congruent.

For the details of the proof, see this link.Write a congruency statement for the two triangles at right. I can identify congruent parts of a polygon, given a congruency statement List ALL of the congruent parts if. Question: Write a congruency statement for the pair of triangles Find the values of x and y. Show your work. Show your work. Show transcribed image text Write a congruency statement for the pair of triangles Find the values of x and y. You can write a single congruence statement about the triangles that shows the correspondence between the two figures.

For the triangles Write a triangle congruence statement for the triangles. 2. Triangle ABC has coordinates A (1, 28), B (5, 24), and C (8, 29). a. LESSON Practice B Triangle Congruence: SSS and SAS Write which of the SSS or SAS postulates, if either, can be used to prove the triangles congruent.

If no triangles can be proved congruent, write neither. 3 3 4 1. neither 2. SAS 7 7 4 4 6 6 3. neither 4.

## Proving Triangles Congruent by Definition and Side-Side-Side (SSS) - SAS

SSS. Example 4: Decide whether the triangles are congruent. If so, write a congruence statement. Name all ostulates or theorems used to reach our conclusion. Nov 02,  · What is a 'congruence statement?'? It is a geometry question that is asking me to write a congruence statement for figures that can be proved congruent. Can you help??? congruence statements are just statements that say what sides or angles of different triangles are congruent.

Source(s): Pat · 1 decade ago. 2. Thumbs up. monstermanfilm.com: Resolved.

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