Question

9 choose the options that best fit the blank boxes. (1 point) given rectangle jklm prove jl ≅ mk it is given that jklm is a rectangle. by the definition of a rectangle, ∠jml and ∠klm are right - angles. and because all right angles are congruent, ∠jml ≅ ∠klm and ml ≅ ml by the reflexive property of congruence. also, opposite sides of rectangle are congruent. by the sas congruence postulate, △jml ≅ △klm. parts of congruent triangles are congruent. jl ≅ mk sas congruence postulate reflexive property of congruence opposite sides of rectangle are congruent definition of a rectangle

Explanation:

Step1: Define rectangle property

By the definition of a rectangle, all angles are right - angles. So for the first blank, the reason for $\angle JML$ and $\angle KLM$ being right - angles is the definition of a rectangle.

Step2: Identify side congruence

In rectangle $JKLM$, opposite sides are congruent. So for the second blank, when considering sides related to the triangles formed, the property used is that opposite sides of a rectangle are congruent.

Step3: Recall congruence property

The statement $ML\cong ML$ is due to the reflexive property of congruence. So for the third blank, the reason is the reflexive property of congruence.

Step4: Apply congruence postulate

To prove $\triangle JML\cong\triangle KLM$, since we have two sides and the included angle (right - angle) congruent, we use the SAS (Side - Angle - Side) congruence postulate. So for the fourth blank, the reason is the SAS congruence postulate.

Answer:

1. definition of a rectangle
2. opposite sides of rectangle are congruent
3. reflexive property of congruence
4. SAS congruence postulate