Corresponding Parts of Congruent Triangles

Front

What are corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are sides and angles that are in the same relative position in each triangle. If two triangles are congruent, their corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' means 'is congruent to'. It indicates that two figures have the same shape and size.

Front

If ΔABC ≅ ΔDEF, what can we conclude about the sides and angles?

Back

We can conclude that side AB = side DE, side BC = side EF, side AC = side DF, and angle A = angle D, angle B = angle E, angle C = angle F.

Front

How do you determine if two triangles are congruent?

Back

Two triangles can be determined to be congruent using criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles).

Front

What is the importance of the order of vertices in triangle congruence?

Back

The order of vertices is important because it indicates which angles and sides correspond to each other. For example, if ΔABC ≅ ΔDEF, then A corresponds to D, B to E, and C to F.

Front

Given that ΔPQR ≅ ΔLJK, if PR = 2x + 6 and JL = 10, find PR when x = 12.

Back

PR = 2(12) + 6 = 30.

Front

If angle XZY measures 48º in triangle XYZ, what is the measure of angle XZY in triangle ABC if ΔXYZ ≅ ΔABC?

Back

The measure of angle XZY in triangle ABC is also 48º.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have exactly the same size and shape, meaning all corresponding sides and angles are equal.

Front

If ΔLMK ≅ ΔLMT, what can we say about the angles and sides of these triangles?

Back

We can say that angle L = angle L, side LM = side LM, side LK = side LT, and side MK = side MT.

Front

What is the Side-Angle-Side (SAS) congruence criterion?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is equal, then the triangles are congruent.