IM Geometry Unit 2 Lesson 14
Here is a diagram of an isosceles triangle APB with segment AP congruent to segment BP.
Here is a valid proof that the angle bisector of the vertex angle of an isosceles triangle is a line of symmetry.
Read the proof and annotate the diagram with each piece of information in the proof.
because triangle APB is isosceles.
The angle bisector of intersects . Call that point Q.
By the definition of an angle bisector, .
because it is the same segment
By SAS .
Therefore, and are corresponding and congruent segments (CPCTC)
and and are corresponding and congruent angles. (CPCTC)
Since and are both congruent and supplementary, both angles are right angles.
So must be the perpendicular bisector of .
What rigid transformation will show ?
IM G Unit 2 Lesson 14 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/2/14/index.html. Licensed under the Creative Commons Attribution 4.0 license, https://creativecommons.org/licenses/by/4.0/.