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Ashraf82

Answer:

63) The additional information is GD ≅ CD

64) The additional information is ∠LQR ≅ ∠PQR

Step-by-step explanation:

  • SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
  • SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ  

Let us use the facts above to solve the questions

#63

In triangles BGD and BCD

∵ BG = BC

∵ BD is a common side

  • To prove that the 2 triangles are congruent using the SSS postulate, then the 3rd sides in the two triangles must be equal

∵ The 3rd sides are GD and CD

∴ GD and CD must be equal

∴ GD = CD

∴ The additional information is GD ≅ CD

#64

In triangles LQR and PQR

∵ LQ = PQ

∵ QR is a common side

  • To prove that the 2 triangles are congruent using the SAS postulate, then the included angles between the congruent sides must be equal

∵ The included angles are ∠LQR and ∠PQR

∴  m∠LQR and m∠PQR must be equal

∴ ∠LQR ≅ ∠PQR

∴ The additional information is ∠LQR ≅ ∠PQR

The additional information required in order to know that the triangles are congruent for the reasons given are;

63) DC ≅ DG

63) DC ≅ DG64) ∠LQR ≅ ∠PQR

63) The congruence theorem used here is SSS. This denotes Side - Side - Side. What this means is that the 3 corresponding sides of ΔBGD and ΔBCD are congruent.

Now, we are given;

BC ≅ BG

Also; BD ≅ BD (By reflexive property)

For the SSS congruence theorem to hold, it means that; DC ≅ DG

64) The congruence theorem used here is SAS. This denotes Side - Angle - Side. What this means is that 2 corresponding sides and the Included of ΔBGD and ΔBCD are congruent.

Now, we are given;

QP ≅ QL

Also; QR ≅ QR (By reflexive property)

The included angles here are ∠LQR and ∠PQR.

Thus, ∠LQR ≅ ∠PQR.

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