Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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If CDE = KLM, find each measure.
![### Topic: Congruent Triangles
#### Problem Statement:
If ∆CDE ≅ ∆KLM, find each measure.
#### Diagrams and Given Measurements:
Two triangles are shown, ∆CDE and ∆KLM.
- In ∆CDE:
- Side CD = 13 mm
- Side DE = 15 mm
- Side CE = 12 mm
- Angle CDE = 74°
- Angle DEC = 59°
- In ∆KLM:
- The sides and angles need to be determined.
#### Objectives:
Find the following measures in ∆KLM:
1. \( m\angle K \)
2. \( m\angle L \)
3. \( \overline{KM} \)
4. \( \overline{LK} \)
#### Explanation:
Since ∆CDE ≅ ∆KLM, the corresponding sides and angles are equal. Therefore:
1. \( m\angle K \) is the angle corresponding to angle CDE (74°).
2. \( m\angle L \) is the angle corresponding to angle DEC (59°).
3. \( \overline{KM} \) is the side corresponding to side DE (15 mm).
4. \( \overline{LK} \) is the side corresponding to side CD (13 mm).
#### Solution:
- \( m\angle K = 74° \)
- \( m\angle L = 59° \)
- \( \overline{KM} = 15 \) mm
- \( \overline{LK} = 13 \) mm
### Exercises:
Verify if your answers correspond with the congruent properties of triangles and check for consistency with other given measures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28bd164b-15c0-4281-9396-dc8e872bf440%2F73e6f33b-207d-48e8-abb2-834ba66932fd%2Fhjnfnoc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Topic: Congruent Triangles
#### Problem Statement:
If ∆CDE ≅ ∆KLM, find each measure.
#### Diagrams and Given Measurements:
Two triangles are shown, ∆CDE and ∆KLM.
- In ∆CDE:
- Side CD = 13 mm
- Side DE = 15 mm
- Side CE = 12 mm
- Angle CDE = 74°
- Angle DEC = 59°
- In ∆KLM:
- The sides and angles need to be determined.
#### Objectives:
Find the following measures in ∆KLM:
1. \( m\angle K \)
2. \( m\angle L \)
3. \( \overline{KM} \)
4. \( \overline{LK} \)
#### Explanation:
Since ∆CDE ≅ ∆KLM, the corresponding sides and angles are equal. Therefore:
1. \( m\angle K \) is the angle corresponding to angle CDE (74°).
2. \( m\angle L \) is the angle corresponding to angle DEC (59°).
3. \( \overline{KM} \) is the side corresponding to side DE (15 mm).
4. \( \overline{LK} \) is the side corresponding to side CD (13 mm).
#### Solution:
- \( m\angle K = 74° \)
- \( m\angle L = 59° \)
- \( \overline{KM} = 15 \) mm
- \( \overline{LK} = 13 \) mm
### Exercises:
Verify if your answers correspond with the congruent properties of triangles and check for consistency with other given measures.
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