Homework Help is Here – Start Your Trial Now!
Math
Geometry
ADEF and APQR are shown below: VA P R F A teacher writes the following 2-column proof on the board. Statement Reason ZE and 2Q are right angles Given A DEF and APQR are right triangles Definition of right triangle DF = PR Given DE = QR Given A DEF = A PQR ? What is the missing reason? Side-Side-Side Triangle Congruence Theorem Hypotenuse-Leg Triangle Congruence Theorem Angle-Side-Angle Triangle Congruence Theorem

ADEF and APQR are shown below: VA P R F A teacher writes the following 2-column proof on the board. Statement Reason ZE and 2Q are right angles Given A DEF and APQR are right triangles Definition of right triangle DF = PR Given DE = QR Given A DEF = A PQR ? What is the missing reason? Side-Side-Side Triangle Congruence Theorem Hypotenuse-Leg Triangle Congruence Theorem Angle-Side-Angle Triangle Congruence Theorem

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question
### Educational Explanation of Triangle Congruence #### Given Problem: We have two triangles, \( \triangle DEF \) and \( \triangle PQR \), displayed in a diagram. Each triangle has a right angle, marked at vertices \( E \) and \( Q \), respectively. The sides are marked such that \( \overline{DF} \cong \overline{PR} \) and \( \overline{DE} \cong \overline{QR} \). #### Two-Column Proof: | Statement | Reason | |----------------------------------------|------------------------------------| | \( \angle E \) and \( \angle Q \) are right angles | Given | | \( \triangle DEF \) and \( \triangle PQR \) are right triangles | Definition of right triangle | | \( \overline{DF} \cong \overline{PR} \) | Given | | \( \overline{DE} \cong \overline{QR} \) | Given | | \( \triangle DEF \cong \triangle PQR \) | ? | #### Missing Reason: The missing reason is the **Hypotenuse-Leg Triangle Congruence Theorem**. This theorem states that two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle. #### Conclusion: With the right angle, congruent hypotenuses \( \overline{DF} \) and \( \overline{PR} \), and congruent legs \( \overline{DE} \) and \( \overline{QR} \), \( \triangle DEF \cong \triangle PQR \) by the Hypotenuse-Leg Triangle Congruence Theorem. For more information on triangle congruence theorems and proofs, please refer to relevant educational resources.
Transcribed Image Text:### Educational Explanation of Triangle Congruence #### Given Problem: We have two triangles, \( \triangle DEF \) and \( \triangle PQR \), displayed in a diagram. Each triangle has a right angle, marked at vertices \( E \) and \( Q \), respectively. The sides are marked such that \( \overline{DF} \cong \overline{PR} \) and \( \overline{DE} \cong \overline{QR} \). #### Two-Column Proof: | Statement | Reason | |----------------------------------------|------------------------------------| | \( \angle E \) and \( \angle Q \) are right angles | Given | | \( \triangle DEF \) and \( \triangle PQR \) are right triangles | Definition of right triangle | | \( \overline{DF} \cong \overline{PR} \) | Given | | \( \overline{DE} \cong \overline{QR} \) | Given | | \( \triangle DEF \cong \triangle PQR \) | ? | #### Missing Reason: The missing reason is the **Hypotenuse-Leg Triangle Congruence Theorem**. This theorem states that two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle. #### Conclusion: With the right angle, congruent hypotenuses \( \overline{DF} \) and \( \overline{PR} \), and congruent legs \( \overline{DE} \) and \( \overline{QR} \), \( \triangle DEF \cong \triangle PQR \) by the Hypotenuse-Leg Triangle Congruence Theorem. For more information on triangle congruence theorems and proofs, please refer to relevant educational resources.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS