Congruent tTiangles Worksheet

In geometry, two figures are congruent if they have the same shape and size. More formally, 2 sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections.

(Source-Wikipedia)

Congruent triangles worksheet -Example 1:

Let PQRS be a parallelogram and PR be one of its diagonals. What can you say about triangles PQRC andRSP?

Solution:
Step 1: In a four-sided figure, opposite sides are congruent. Hence sides

Step 2: QR and PS are congruent, and also sides PQ and RS are congruent.
Step 3: In a four-sided figure opposite angles are congruent.

Step 4: Hence angles PQR and RSP  are  four side figure.
Step 5: Two sides and an included angle of triangle PQR are congruent to two corresponding sides and an included angle in triangle RSP. According to the above postulate the two triangles PQR and RSP are congruent.

Congruent triangles worksheet-Example 2:

To solve the  triangle ABC congruent to triangle EFV by SAS?

Solution:
Step 1:Segment AB is congruent
Step 2: To segment of ST is
Step 3:  AB = EF = 4.
Step 4: Angle B is congruent to
Step 5: angle T because angle B = angle F = 100 degrees.
Step 6:Segment BC is congruent to segment FV because BC = FV = 5.
Step 7: ABC is congruent EFV is a SAS.



Congruent triangles worksheet-Example 3:
To solve the angle is QR is congruent to angle ST.

Solution:
Step 1: The triangle RPQ is congruent to triangle RTS.             
Step 2: Angle P is congruent to angle S because that information is given  in the diagram.
Step 3: Segment PR is congruent to segment RS because that information is given in the diagram.
Step 4: Angle QRP is congruent to angle SRT because vertical angles are congruent.
Step 5: Triangle SPQ is congruent to triangle RTS by Angle-Side-Angle.
Step 6: The triangles arecongruent, you know that all orresponding parts must be congruent.
Step 7:By CPCTC, segment BC is congruent to segment CE.