Question

1. match the correct answers. given: mnop is a kite. prove: ∠n ≅ ∠p statements reasons 1. mnop is a kite. 1. given 2. $overline{mn} cong overline{mp}$; $overline{no} cong overline{po}$ 2. def. of a 3. $overline{mo} cong overline{mo}$ 3. 4. 4. 5. ∠n ≅ ∠p 5. a. sss b. cpctc c. sas d. reflexive property of ≅ e. kite f. rhombus g. $\triangle mno cong \triangle mpo$ h. symmetric property of ≅

Explanation:

Step1: Analyze Reason 2

A kite is defined as a quadrilateral with two distinct pairs of adjacent sides that are congruent. So the reason for $\overline{MN} \cong \overline{MP}$ and $\overline{NO} \cong \overline{PO}$ is the definition of a kite. So we choose option e (kite) for Reason 2.

Step2: Analyze Reason 3

The statement $\overline{MO} \cong \overline{MO}$ is saying a segment is congruent to itself, which is the Reflexive Property of Congruence. So we choose option d (Reflexive Property of $\cong$) for Reason 3.

Step3: Analyze Statement 4 and Reason 4

We have three sides: $\overline{MN} \cong \overline{MP}$, $\overline{NO} \cong \overline{PO}$, and $\overline{MO} \cong \overline{MO}$. By the SSS (Side - Side - Side) congruence criterion, we can say that $\triangle MNO \cong \triangle MPO$. So Statement 4 is $\triangle MNO \cong \triangle MPO$ (option g) and Reason 4 is SSS (option a).

Step4: Analyze Reason 5

Since $\triangle MNO \cong \triangle MPO$, the corresponding parts (angles $\angle N$ and $\angle P$) are congruent. This is the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem. So we choose option b (CPCTC) for Reason 5.

Answer:

• Reason 2: e. kite
• Reason 3: d. Reflexive Property of $\cong$
• Statement 4: g. $\triangle MNO \cong \triangle MPO$; Reason 4: a. SSS
• Reason 5: b. CPCTC