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 statements shows. 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 correctly shows that a diagonal of kite WXYZ decomposes it into two congruent triangles, we can analyze each statement separately using properties of congruence and theorems for triangles.
1. Statement 1:
- In kite WXYZ, WX is congruent to WZ, and YX is congruent to YZ.
- It states that triangle WYZ is congruent to triangle WYX by the Side-Side-Side (SSS) Triangle Congruence Theorem.
- This means all three sides of triangle WYZ are congruent to the corresponding sides of triangle WYX.
- Since the SSS Theorem is a valid method for proving two triangles are congruent, this statement is correct in showing that diagonal WY decomposes the kite into two congruent triangles.
2. Statement 2:
- This statement claims congruence by the "Side-Side" theorem, which is not a valid method as it lacks a necessary third condition (like another side or angle).
- Therefore, it doesn't successfully prove congruence between the triangles.
3. Statement 3:
- This statement uses the Side-Angle-Side (SAS) Triangle Congruence Theorem.
- However, without specifying which angles are congruent or providing sufficient evidence, we can't confirm this statement as accurately supporting its claim.
4. Statement 4:
- This statement uses the Angle-Side-Angle (ASA) Triangle Congruence Theorem.
- It provides an angle, a side, and another angle. However, the congruence of segments alone (like WY = WY) isn't enough without the correct pairs of congruent angles being specified for ASA to be valid.
Given these analyses, Statement 1 correctly uses the Side-Side-Side Triangle Congruence Theorem, proving that diagonal WY in kite WXYZ decomposes it into two congruent triangles. Thus, the correct choice is the one that aligns with the first option in the problem.
1. Statement 1:
- In kite WXYZ, WX is congruent to WZ, and YX is congruent to YZ.
- It states that triangle WYZ is congruent to triangle WYX by the Side-Side-Side (SSS) Triangle Congruence Theorem.
- This means all three sides of triangle WYZ are congruent to the corresponding sides of triangle WYX.
- Since the SSS Theorem is a valid method for proving two triangles are congruent, this statement is correct in showing that diagonal WY decomposes the kite into two congruent triangles.
2. Statement 2:
- This statement claims congruence by the "Side-Side" theorem, which is not a valid method as it lacks a necessary third condition (like another side or angle).
- Therefore, it doesn't successfully prove congruence between the triangles.
3. Statement 3:
- This statement uses the Side-Angle-Side (SAS) Triangle Congruence Theorem.
- However, without specifying which angles are congruent or providing sufficient evidence, we can't confirm this statement as accurately supporting its claim.
4. Statement 4:
- This statement uses the Angle-Side-Angle (ASA) Triangle Congruence Theorem.
- It provides an angle, a side, and another angle. However, the congruence of segments alone (like WY = WY) isn't enough without the correct pairs of congruent angles being specified for ASA to be valid.
Given these analyses, Statement 1 correctly uses the Side-Side-Side Triangle Congruence Theorem, proving that diagonal WY in kite WXYZ decomposes it into two congruent triangles. Thus, the correct choice is the one that aligns with the first option in the problem.
Thank you for reading the article A kite is a quadrilateral with two pairs of adjacent sides that are congruent Given kite tex WXYZ tex which of the following statements shows. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
