Question

Determine which congruence theorem or postulate proves the triangles are congruent based on the given information.

Answer 1

The congruence theorem or postulate that proves the triangles are congruent based on the specified information are;

∠A ≅ ∠R,
`\overline{LH}` ≅
`\overline{GD}`, ∠H ≅ ∠D; AAS

`\overline{AH}` ≅
`\overline{RD}`,
`\overline{LA}` ≅
`\overline{GR}`,
`\overline{LH}` ≅
`\overline{GD}`; SSS

`\overline{LA}` ≅
`\overline{GR}`,
`\overline{LH}` ≅
`\overline{GD}`, ∠L ≅ ∠G; SAS

`\overline{AH}` ≅
`\overline{RD}`, ∠H ≅ ∠D, ∠A ≅ ∠R; ASA

What are congruent triangles?; Congruent triangles are triangles that have the same shape and size.

The details of the congruence rules used to prove that the triangles ΔLAH and ΔGRD are congruent are;

Angle Angle Side, AAS

Angle Angle Side, AAS, congruence rule states that if two angles and a side which is non included between the angles in one triangle are congruent to two angles and a non included side in another triangle, then the two triangles are congruent

Side Side Side, SSS

The SSS, which is an acronym for Side Side Side, congruence rule states that if all three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent

Side Angle Side, SAS

The Side Angle Side, SAS, congruence rule states that if two sides and an included angle in one triangle are congruent to two sides and an included angle in another triangle, then the two triangles are congruent

Angle Side Angle, ASA

The Angle Side Angle, ASA, congruence rule states that if two angles and an included side in one triangle are congruent to two angles and an included side in another triangle, then the two triangles are congruent