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a. Write congruence statements for two different pairs of line segments (other than the diagonals.)b. Determine two pairs of congruent triangles and write their corresponding statements. Next to these, write the triangle congruence property that proves they are congruent.

a. Write congruence statements for two different pairs of line segments (other than-example-1
User London Student
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1 Answer

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Given the isosceles trapezoid:

MARK

Diagonals:

MR and AK

Let's answer the following questions.

(b). Determine two pairs of congruent triangles and write their corresponding statements. Next to these, write the triangle congruence property that proves they are congruent.

Here, the two pairs of congruent triangles are:

• ΔMKR and ΔARK

,

• ΔMPK and ΔAPR

• To prove that ,ΔMKR ≅ ΔARK, ,we are to use the Side-Angle-Side Theorem,

The corresponding congruence statements are:

MK ≅ AR: Opposite vertical legs of an isosceles trapezoid have the same lengths

∠MKR ≅ ∠ARK: Base angles of an isosceles trapezoid are congruent.

KR ≅ RK: By reflexive property.

Therefore, we can say ΔMKR ≅ ΔARK by the Side-Angle-Side (SAS) theorem which states that If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

• To prove that ,ΔMPK ≅ ΔAPR, ,we are to use the Angle-Side-Angle (ASA) theorem.

The corresponding congruence statements are:

∠KMP ≅ ∠RAP: Diagonals in an isosceles trapezoid bisect the angles.

MK ≅ AR: Opposite vertical legs of an isosceles trapezoid have the same lengths

∠MKP ≅ ∠ARP: Diagonals in an isosceles trapezoid bisect the angles.

Therefore, we can say ΔMPK ≅ ΔAPR by the Angle-Side-Angle theorem which states that if two angles and the included side of one triangle are equal to the two angles and included side of another triangle, both triangles are congruent.

User Sarel
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