State what additional information is required in order to know that the triangles are congruent for the reason given

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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63) The additional information is GD ≅ CD

64) The additional information is ∠LQR ≅ ∠PQR

Step-by-step explanation:

Let us use the facts above to solve the questions

#63

In triangles BGD and BCD

∵ BG = BC

∵ BD is a common side

∵ 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

∵ The included angles are ∠LQR and ∠PQR

∴  m∠LQR and m∠PQR must be equal

∴ ∠LQR ≅ ∠PQR

∴ The additional information is ∠LQR ≅ ∠PQR

40 is the final : )

3-4

step-by-step explanation:

the answer is 3-4 because both 45 and 60 has a multiple of 15.

45/3=15

60/4=15

therefore the odds against selecting a red is 4-3