Sage-Tips

Which theorem proves that the triangles are congruent?

Angle-Side-Angle Theorem
Explanation: The Angle-Side-Angle Theorem (ASA) states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent.

How do you know which congruence theorem to use?

If the hypotenuse and one of the legs (sides) of a right triangle are congruent to hypotenuse and corresponding leg of the other right triangle, the two triangles are said to be congruent. If all three sides of a triangle are congruent to corresponding three sides of other triangle then the two triangles are congruent.

Which congruence theorem can be used to prove triangle ABC is congruent to triangle DEC?

Side-Angle-Side (SAS) 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. Using labels: If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.

What are the congruence theorem?

There are three very useful theorems that connect equality and congruence. Two angles are congruent if and only if they have equal measures. Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

Which of triangles ABC and D is congruent to triangle E?

If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AB = DE, then triangle ABC is congruent to triangle DEF.

Is triangle MNL congruent to triangle Qnl?

Is MNL ≅ QNL? Why or why not? A. Yes, they are congruent by either ASA or AAS.

What are the three methods of proving triangles congruent?

Methods of proving triangles are congruent: Side-Side-Side (SSS) – we have to prove that all three sides are congruent. Side-Angle-Side (SAS) – what’s very important here is that the “Angle” is written between the two sides. Angle-Side-Angle (ASA) – just like the “angle” in SAS is in between two sides; the “Side” here should also be in between two angles.

How do you prove triangle congruence?

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. A second way to prove the congruence of triangles is to show that two sides and their included angle are congruent.

How are congruent triangles used in real life?

Construction. Congruent triangles are used in the construction to reinforce the structure. This ensures that the structures are strong and rigid.

Truss Bridge. A truss bridge is formed by equilateral triangles on both sides. All these triangles are congruent under the SSS criteria.

Geodesic Dome. This is common playground equipment.

How to prove if some triangles are congruent?

Side-side-side (SSS): both triangles have three sides that equal to each other. Side-angle-side (SAS): two sides of the triangle and their included angle (the angle between the two sides) are equal in both triangles. Angle-side-angle (ASA): two angles of each triangle and their included side are equal.