Homework Help is Here – Start Your Trial Now!
Math
Geometry
64 64° 77° 49 H. D. 39 K 39 77° E 49° 'F Which pair of triangles is similar? O ABCA ~ AEDF O ADFE ~ AKML O AMKL ~ AHGJ 2. O AACB ~ AGHJ

64 64° 77° 49 H. D. 39 K 39 77° E 49° 'F Which pair of triangles is similar? O ABCA ~ AEDF O ADFE ~ AKML O AMKL ~ AHGJ 2. O AACB ~ AGHJ

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
**Which pair of triangles is similar?** There are four triangles labeled with their corresponding angles. Here are the details of each triangle: 1. Triangle BCA: - \( \angle B = 64^\circ \) - \( \angle C = 77^\circ \) 2. Triangle EDf: - \( \angle D = 39^\circ \) - \( \angle E = 77^\circ \) 3. Triangle KLM: - \( \angle K = 39^\circ \) - \( \angle L = 64^\circ \) - \( \angle M = 49^\circ \) 4. Triangle GHJ: - \( \angle H = 49^\circ \) - \( \angle J = 64^\circ \) The question asks which pair of triangles is similar. **Answer choices:** - ○ \( \triangle BCA \sim \triangle EDF \) - ○ \( \triangle DFE \sim \triangle KML \) - ○ \( \triangle MKL \sim \triangle HGJ \) - ○ \( \triangle ACB \sim \triangle GHJ \) **Explanation of the diagrams:** 1. **Triangle BCA** has angles of 64° and 77°. The third angle, which can be determined by subtracting the sum of the known angles from 180°, is 39°. 2. **Triangle EDF** has angles of 39° and 77°. The third angle, which can be determined similarly, is 64°. 3. **Triangle KML** has angles of 39°, 49°, and 64°. 4. **Triangle GHJ** has angles of 49° and 64°. The third angle, which can be determined similarly, is 67°. Using the angle-angle (AA) similarity criterion, we compare the triangles based on their angles: - Comparing \(\triangle BCA\) and \(\triangle EDF\), both have angles of 39°, 64°, and 77°, indicating similarity. Therefore, the correct answer is: - ○ \( \triangle BCA \sim \triangle EDF \)
Transcribed Image Text:**Which pair of triangles is similar?** There are four triangles labeled with their corresponding angles. Here are the details of each triangle: 1. Triangle BCA: - \( \angle B = 64^\circ \) - \( \angle C = 77^\circ \) 2. Triangle EDf: - \( \angle D = 39^\circ \) - \( \angle E = 77^\circ \) 3. Triangle KLM: - \( \angle K = 39^\circ \) - \( \angle L = 64^\circ \) - \( \angle M = 49^\circ \) 4. Triangle GHJ: - \( \angle H = 49^\circ \) - \( \angle J = 64^\circ \) The question asks which pair of triangles is similar. **Answer choices:** - ○ \( \triangle BCA \sim \triangle EDF \) - ○ \( \triangle DFE \sim \triangle KML \) - ○ \( \triangle MKL \sim \triangle HGJ \) - ○ \( \triangle ACB \sim \triangle GHJ \) **Explanation of the diagrams:** 1. **Triangle BCA** has angles of 64° and 77°. The third angle, which can be determined by subtracting the sum of the known angles from 180°, is 39°. 2. **Triangle EDF** has angles of 39° and 77°. The third angle, which can be determined similarly, is 64°. 3. **Triangle KML** has angles of 39°, 49°, and 64°. 4. **Triangle GHJ** has angles of 49° and 64°. The third angle, which can be determined similarly, is 67°. Using the angle-angle (AA) similarity criterion, we compare the triangles based on their angles: - Comparing \(\triangle BCA\) and \(\triangle EDF\), both have angles of 39°, 64°, and 77°, indicating similarity. Therefore, the correct answer is: - ○ \( \triangle BCA \sim \triangle EDF \)
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Factorization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
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