### Developing ProofComplete the proof by filling in the blanks.**Given:**$\angle H IJ \cong \angle K I$$\angle J H \cong \angle I J K$**Prove:**$\Delta H IJ \cong \Delta K IJ$**Proof:**$\angle H IJ \cong \angle K IJ$ and $\angle J H \cong \angle I J K$ are given.$IJ = IJ$ by _(1)_.So, $\Delta H IJ \cong \Delta K IJ$ by _(2)_.**Key:**1. Reflexive property of equality.2. ASA postulate (Angle-Side-Angle).**Diagram:**The diagram accompanying the proof shows two triangles, $\Delta HIJ$ and $\Delta KIJ$, sharing a common side $IJ$. The angles $\angle HIJ$ and $\angle KIJ$ are marked as congruent, as well as the angles $\angle JH$ and $\angle IJK$.1. **$\angle HIJ \cong \angle KIJ$:** This specifies that the angles $HIJ$ and $KIJ$ are congruent.2. **$\angle JH \cong \angle IJK$:** This specifies that the angles $JH$ and $IJK$ are congruent.3. **$IJ = IJ$ by the Reflexive property:** Indicates that the shared side $IJ$ is equal to itself by the Reflexive property of equality.By using these points, the proof concludes that $\Delta HIJ \cong \Delta KIJ$ by the ASA (Angle-Side-Angle) postulate, a method of proving the congruence of triangles.

Name: ### Developing ProofComplete the proof by filling in the blanks.**Giv
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Description: ### Developing ProofComplete the proof by filling in the blanks.**Given:**$\angle H IJ \cong \angle K I$$\angle J H \cong \angle I J K$**Prove:**$\Delta H IJ \cong \Delta K IJ$**Proof:**$\angle H IJ \cong \angle K IJ$ and \(\angle J H \cong

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3. Developing Proof Complete tho proof by filling in the blanks. K Given: HIJ ZKI AJH LIJK Prove: AHIJ AKIJ H Proof: HIJ ZKIJ and ZIJH a LIJK are given. = J by ?- So, AHIJ AKIJ by_?.

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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### Developing Proof

Complete the proof by filling in the blanks.

**Given:**

$\angle H IJ \cong \angle K I$

$\angle J H \cong \angle I J K$

**Prove:**

$\Delta H IJ \cong \Delta K IJ$

**Proof:**

$\angle H IJ \cong \angle K IJ$ and $\angle J H \cong \angle I J K$ are given.

$IJ = IJ$ by _(1)_.

So, $\Delta H IJ \cong \Delta K IJ$ by _(2)_.

**Key:**
1. Reflexive property of equality.
2. ASA postulate (Angle-Side-Angle).

**Diagram:**

The diagram accompanying the proof shows two triangles, $\Delta HIJ$ and $\Delta KIJ$, sharing a common side $IJ$. The angles $\angle HIJ$ and $\angle KIJ$ are marked as congruent, as well as the angles $\angle JH$ and $\angle IJK$.

1. **$\angle HIJ \cong \angle KIJ$:** This specifies that the angles $HIJ$ and $KIJ$ are congruent.
2. **$\angle JH \cong \angle IJK$:** This specifies that the angles $JH$ and $IJK$ are congruent.
3. **$IJ = IJ$ by the Reflexive property:** Indicates that the shared side $IJ$ is equal to itself by the Reflexive property of equality.

By using these points, the proof concludes that $\Delta HIJ \cong \Delta KIJ$ by the ASA (Angle-Side-Angle) postulate, a method of proving the congruence of triangles.

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