Thank you for visiting A kite is a quadrilateral with two pairs of adjacent sides that are congruent Given kite tex WXYZ tex which of the following shows that. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine which statement shows that at least one of the diagonals of a kite decomposes the kite into two congruent triangles, let's review the options.
Understanding the structure of a kite:
A kite is a quadrilateral with two pairs of adjacent sides that are congruent. In kite WXYZ:
- [tex]\(WX\)[/tex] is congruent to [tex]\(WZ\)[/tex]
- [tex]\(YX\)[/tex] is congruent to [tex]\(YZ\)[/tex]
We need to check which statement correctly explains that one of the diagonals splits the kite into two congruent triangles.
Option A Analysis:
1. In kite WXYZ, the sides [tex]\(WX\)[/tex] and [tex]\(WZ\)[/tex] are congruent, and [tex]\(YX\)[/tex] and [tex]\(YZ\)[/tex] are congruent.
2. Diagonal [tex]\(WY\)[/tex] is common to both triangles [tex]\(\triangle WYZ\)[/tex] and [tex]\(\triangle WYX\)[/tex].
3. The sides [tex]\(WX = WZ\)[/tex], [tex]\(YX = YZ\)[/tex], and [tex]\(WY = WY\)[/tex] (common side).
4. By the Side-Side-Side (SSS) Triangle Congruence Theorem, [tex]\(\triangle WYZ\)[/tex] is congruent to [tex]\(\triangle WYX\)[/tex].
Therefore, option A correctly shows that diagonal [tex]\(WY\)[/tex] decomposes the kite into two congruent triangles.
Options B, C, and D appear to contain errors or incorrect applications of congruence theorems. Option A uses the properties and congruence theorems correctly, ensuring that at least one diagonal divides the kite into two congruent triangles. Thus, the correct answer is option A.
Understanding the structure of a kite:
A kite is a quadrilateral with two pairs of adjacent sides that are congruent. In kite WXYZ:
- [tex]\(WX\)[/tex] is congruent to [tex]\(WZ\)[/tex]
- [tex]\(YX\)[/tex] is congruent to [tex]\(YZ\)[/tex]
We need to check which statement correctly explains that one of the diagonals splits the kite into two congruent triangles.
Option A Analysis:
1. In kite WXYZ, the sides [tex]\(WX\)[/tex] and [tex]\(WZ\)[/tex] are congruent, and [tex]\(YX\)[/tex] and [tex]\(YZ\)[/tex] are congruent.
2. Diagonal [tex]\(WY\)[/tex] is common to both triangles [tex]\(\triangle WYZ\)[/tex] and [tex]\(\triangle WYX\)[/tex].
3. The sides [tex]\(WX = WZ\)[/tex], [tex]\(YX = YZ\)[/tex], and [tex]\(WY = WY\)[/tex] (common side).
4. By the Side-Side-Side (SSS) Triangle Congruence Theorem, [tex]\(\triangle WYZ\)[/tex] is congruent to [tex]\(\triangle WYX\)[/tex].
Therefore, option A correctly shows that diagonal [tex]\(WY\)[/tex] decomposes the kite into two congruent triangles.
Options B, C, and D appear to contain errors or incorrect applications of congruence theorems. Option A uses the properties and congruence theorems correctly, ensuring that at least one diagonal divides the kite into two congruent triangles. Thus, the correct answer is option A.
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Rewritten by : Jeany
