Answer the Following:

Question

Line BT is perpendicular bisector of segment HQ. Explain why angle H is congruent to angle Q.

Answer 1

Why not use SAS, instead?

Take the first two points from Philip; then, as it is a perpendicular bisector,

both BTH and BTQ have measure 90°, so these angles are congruent.

Thus, from SAS, the triangles are congruent,

Thus, angle H is congruent to angle Q

Answer 2

Given BT perpendicular to HQ

So according to the theorem, every point on the perpendicular bisector will be equidistant from the end points of the segment.

BH congruent to BQ

therefore triangle BHQ is isosceles

<H congruent to <Q - base angles in an isosceles triangle are congruent

hope this helps!

Answer 3

You can show that triangle HTB is congruent to triangle QTB by SSS congruence. That means that angle H will be congruent to angle Q because corresponding parts of congruent triangles are congruent (CPCTC).

We know:

1. HT≅ QT because BT bisects HQ into two equal segments
2. BT ≅ BT by the Reflexive Property (a quantity is congruent with itself)
3. HB ≅ QB because any point on the perpendicular bisector (B) is equidistant from the endpoints of the segment (HQ)

Hence triangle HTB is congruent to triangle QTB by SSS congruence and angle H is congruent to angle Q by CPCTC.