Line m is a perpendicular bisector of line segment S Q. It intersects line segment S Q at point R. Line m also contains points T and V. Line segment T S is 3 x + 2. Line segment S V is 4 x minus 1. What is the length of segment TQ?

14 units

Step-by-step explanation:

In the diagram, the length of segment QV is 15 units. What is the length of segment TQ?

Solution:

A triangle is a shape with three sides and three angles. Types of triangles are isosceles triangle, equilateral triangle, scalene triangle, right angled triangle.

Two triangles are said to be congruent if all the corresponding three sides and three angles of one triangle is equal to the corresponding three sides and three angles of the other triangle.

Triangle SRV and triangle RQV are congruent triangles by side angle side congruency (i.e. SR = RQ, RV ≅ RV and ∠SRV = ∠QRV = 90°). Therefore:

SV = QV

4x - 1 = 15

4x = 16

x = 4 units

Triangle SRT and triangle RQT are congruent triangles by side angle side congruency (i.e. SR = RQ, TR ≅ TR and ∠SRT = ∠QRT = 90°). Therefore:

TQ = TS

3x + 2 = TS

TS = 3(4) + 2 = 12 + 2

TS = 14 units