Congruence Of Triangles

Answer

Step 1: Check the given parts. Two sides are equal: AB = DE and BC = EF. Step 2: The angle between those sides is also equal: ∠B = ∠E. Step 3: This matches SAS. Conclusion: △ABC ≅ △DEF by SAS.

Answer

Step 1: Match the vertices in order. P ↔ X, Q ↔ Y, R ↔ Z. Step 2: Write corresponding sides. PQ = XY, QR = YZ, PR = XZ. Step 3: Write corresponding angles. ∠P = ∠X, ∠Q = ∠Y, ∠R = ∠Z. Conclusion: Verte…

Answer

The order tells the correspondence of parts. For example, △PQR ≅ △XYZ means P ↔ X, Q ↔ Y, and R ↔ Z. If the order changes, the matching of sides and angles also changes. So △PQR ≅ △XYZ is not the same…

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Step 1: Look at the given information. Step 2: If two angles and one side of one triangle are equal to the corresponding two angles and side of another triangle, the triangles are congruent. Step 3: T…

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Step 1: Identify the equal sides. AB = AC. Step 2: Use the base angles theorem. If two sides of a triangle are equal, then the angles opposite to them are also equal. Step 3: The angle opposite AB is …

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Step 1: Identify the equal angles. ∠B = ∠C. Step 2: Use the converse theorem. If two angles of a triangle are equal, then the sides opposite to them are also equal. Step 3: The sides opposite ∠B and ∠…

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Step 1: In an equilateral triangle, all sides are equal. Step 2: Equal sides give equal opposite angles, so all three angles are equal. Step 3: The sum of angles in a triangle is 180°. Step 4: 180° ÷ …

Answer

Step 1: Two angles are equal: 62° and 62°. Step 2: Sides opposite equal angles are equal. Step 3: The side opposite 56° is the shortest among the three. Conclusion: BC < AC = AB.