Students' conceptions of the definitions of congruent and similar triangles*

Author(s):  
Aehsan Haj-Yahya
Keyword(s):  
1939 ◽  
Vol 23 (255) ◽  
pp. 335
Author(s):  
F. J. Wood ◽  
G. H. Grattan-Guinness
Keyword(s):  

2007 ◽  
Vol 23 (1-2) ◽  
pp. 321-327
Author(s):  
Zhanjun Su ◽  
Ren Ding
Keyword(s):  

1995 ◽  
Vol 79 (486) ◽  
pp. 569 ◽  
Author(s):  
Hiroshi Okumura
Keyword(s):  

2014 ◽  
Vol 7 (1) ◽  
Author(s):  
John J. H. Lin ◽  
Sunny S. J. Lin

The present study investigated the following issues: (1) whether differences are evident in the eye movement measures of successful and unsuccessful problem-solvers; (2) what is the relationship between perceived difficulty and eye movement measures; and (3) whether eye movements in various AOIs differ when solving problems. Sixty-three 11th grade students solved five geometry problems about the properties of similar triangles. A digital drawing tablet and sensitive pressure pen were used to record the responses. The results indicated that unsuccessful solvers tended to have more fixation counts, run counts, and longer dwell time on the problem area, whereas successful solvers focused more on the calculation area. In addition, fixation counts, dwell time, and run counts in the diagram area were positively correlated with the perceived difficulty, suggesting that understanding similar triangles may require translation or mental rotation. We argue that three eye movement measures (i.e., fixation counts, dwell time, and run counts) are appropriate for use in examining problem solving given that they differentiate successful from unsuccessful solvers and correlate with perceived difficulty. Furthermore, the eye-tracking technique provides objective measures of students’ cognitive load for instructional designers.


KoG ◽  
2018 ◽  
pp. 3-11
Author(s):  
Boris Odehnal

A semi-orthogonal path is a polygon inscribed into a given polygon such that the $i$-th side of the path is orthogonal to the $i$-th side of the given polygon. Especially in the case of triangles, the closed semi-orthogonal paths are triangles which turn out to be similar to the given triangle. The iteration of the construction of semi-orthogonal paths in triangles yields infinite sequences of nested and similar triangles. We show that these two different sequences converge towards the bicentric pair of the triangle's Brocard points. Furthermore, the relation to discrete logarithmic spirals allows us to give a very simple, elementary, and new constructions of the sequences' limits, the Brocard points. We also add some remarks on semi-orthogonal paths in non-Euclidean geometries and in $n$-gons.


1970 ◽  
Vol 37 (4) ◽  
pp. 1176-1179 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi

Using Cayley’s construction of parallelograms and similar triangles, the existence of the coupler cognate of the geared five-link mechanism is established for the general case in which the coupler point is arbitrarily located in the plane of one of the coupler links. The Cayley diagram for the geared five-link mechanism is proposed. Its extension leads to the coupler cognates of plane, single-loop, geared, multilink mechanisms.


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