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Use the diagrams on pages 153 and 154 to prove the following theorems.Theorem $4-5$

$\overline{A X} \cong \overline{A X}$ - reflexive property$\overline{X B} \cong \overline{X C}-$ property of bisector$\angle A X B \cong \angle A X C$ -both right angles- property of perpendicular lineBy theorem SAS, $A B=A C$

Geometry

Chapter 4

Congruent Triangle

Section 7

Medians, Altitudes, and Perpendicular Bisectors

Congruent Triangles

Relationships Within Triangles

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problem number 14. They want us to prove that a B equals a C. Given that line l is the perpendicular by sector of B C and A is on line ele. All right, so first, we're going to say l is the perpendicular or by sector of a C. Okay, that's given. And also I think we should mention, um, line A X is the same as line l Okay, we can see that from the diagram. And it was given that point A is on the perpendicular by sector. Okay, so we know that be X is congrats. Went to X c. Okay. And that's the definition of bisect. We said a X is perpendicular by sector. Okay. And we know that angle. A xsi and a X B are right angles. Okay? And that's the definition off perpendicular by sector. All right. And because they're both right angles, angle a xsi is congratulate to angle a x B. And that's because all right angles Arkan growing. And we also know that a X is congratulate to itself. All right, that's the reflexive property. Okay, so if I could just draw this right angle in here, we have a side angle side side angle sites. Let's make the letters in order. I'm gonna say triangle be X a is congruent to see x a All right triangle be x A is congratulate to triangle c x a. Okay, so from there we can say that a B equals a c. All right. A B is the 1st and 3rd letters, and a C is the 1st and 3rd letters, so they correspond to each other. So that means a B equals a C. And the reason for that is because could corresponding parts of congruent triangles are congruent, so a B equals a C. Uh, I gotta make three marks. There you go.

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