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.

### If Δ ABC is congruent to Δ DEF by SSS congruence rule, then :

*⇒∠A=∠D,∠B=∠E,∠C=∠F*. Was this answer helpful? upvote 0.

### if triangle ABC=DEF,fill in the blanks to make each statement …

*If*in

*triangles ABC*and

*DEF*, AB = DE, AC = DF, and

*angle*A =

*angle*D, then

*triangle ABC is congruent to triangle DEF*.

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## Is triangle ABC congruent to triangle?

Definition: If triangle ABC is congruent to triangle DEF, then all corresponding angles are congruent, and all corresponding sides are congruent. Note: There are certain conditions that, if met, imply that all corresponding angles and sides are congruent of two triangles.

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## Which theorem justifies the statement △ ABC ≅ △ def?

By the ASA Congruence Theorem, △ABC ≅ △DEF.

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## What if triangle ABC is similar to triangle def?

ABC will be similar to DEF if two sides along with their corresponding angle of ABC is equal to two sides and their corresponding angle of DEF. ABC will be similar to DEF if the corresponding ratios of all sides of both triangles are equal to each other.

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## What is a triangle def congruent?

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

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## Why is triangle ABC congruent to triangle?

Solution. The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.

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## Is triangle ABC similar to triangle?

Triangle ABC is similar to triangle PQR.

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## Is triangle ABC congruent to triangle PQR?

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side BC of Δ ABC so that the two triangles are congruent? Give reason for your answer. Hence, triangle ABC and PQR will be congruent by AAS congruence rule.

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## Is triangle ABC congruent to triangle CDA?

Summary: Triangle ABC is congruent to triangle CDA and it is established by the fulfillment of the condition SAS (two sides and an included angle).

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## Is triangle ABC similar to triangle DEF explain?

So, equiangular triangles are also called similar triangles. For example, triangle DEF is similar to triangle ABC as their three angles are equal. The length of each side in triangle DEF is multiplied by the same number, 3, to give the sides of triangle ABC.

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## Are △ ABC and △ def similar?

sides are equal. Similar Triangles Two triangles △ABC and △DEF are similar (written △ABC ∼ △DEF) if all three corresponding angles are equal. Parallel Lines Two lines are parallel if they do not intersect.

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## Is triangle ABC similar to triangle DEF and triangle ABC is not similar to triangle DEF then which of the following is not true?

Summary: If △ABC ~ △EDF and △ABC is not similar to △DEF, then option (c) BC . DE = AB . EF is not true.

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## What is the scale factor from ABC to DEF similar triangles?

For 2 similar triangles ABC and DEF, the scale factor of ABC to DEF is 2:3.

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## How many corresponding parts are congruent if △ ABC ≅ △ def?

The four triangles are congruent with each other regardless whether they are rotated or flipped. The congruence of two objects is often represented using the symbol “≅”. In the figure below, △ABC ≅ △DEF.

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## Which postulate or theorem proves △ ABC ≅ △ def?

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Use the ASA and AAS Congruence Theorems. are congruent. By the ASA Congruence Theorem, △ABC ≅ △DEF.

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## What does congruent mean in maths?

The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.

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## What are congruent triangles examples?

The Angle – Angle – Side rule (AAS) states that two triangles are congruent if their corresponding two angles and one non-included side are equal. Given that; ∠ BAC = ∠ QPR, ∠ ACB = ∠ RQP and length AB = QR, then triangle ABC and PQR are congruent (△ABC ≅△ PQR).

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