2) In A ABC measure the lengths AB and BC as well as ZB. Now, construct a triangle with these three measurement on a sheet of paper. Place this triangle over AABC. Are the triangles congruent? What criterion of congruency applies over here?
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Answer:
Congruence of Triangles- The chapter focuses on the congruency of plane figures, line segments, angles, and triangles.
Congruent objects are exact copies of one another.
The first section of the chapter deals with congruence of plane figures, congruence among line segments and congruence of angles.
If two line segments have the same (i.e., equal) length, they are congruent. Also, if two line segments are congruent, they have the same length.
If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.
After that, congruence of triangles is discussed. Exercise 7.1 is based on the concept of above cited topics. The other half of the chapter deals with Criteria For the congruence of Triangles. Explanation of criterion is given in an interesting way, they are mentioned in the form of games. Students will be briefed about the following criterion:
1. SSS congruence criteria: Triangles are congruent if three sides of the one are equal to the three corresponding sides of the other.
2. SAS congruence criteria: Triangles are congruent if two sides and the angle included between them in one of the triangle are equal to the corresponding sides and the angle included between them of the other triangle.
3. ASA congruence criteria: Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.
Emphasis will also be laid upon the topic- Congruence Among Right-Angled Triangles.
RHS congruence criteria: If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.
Later the chapter Congruence of Triangles concludes with a summary.
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