Discussion
In triangles ABC and DEF, ∠C = ∠F, AC = DF, and BC = EF. If AB = 2x - 1 and DE = 5x - 4, then the value of x is
Answer: A
The value of x is 1.
In the two triangles, AC = DF, BC = EF, and the included angles ∠C and ∠F are equal. By the SAS (side-angle-side) congruence rule, triangle ABC is congruent to triangle DEF, so the third sides are equal: AB = DE.
\[ \begin{aligned} 2x - 1 &= 5x - 4 \\ 3 &= 3x, \quad x = 1 \end{aligned} \]
Check: AB = 2(1) - 1 = 1 and DE = 5(1) - 4 = 1. Any other value of x would make AB and DE unequal, which the congruence rules out.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development