Question

Question 1 options:

m∠A = _____˚

m∠B = _____˚

m∠C = _____˚

m∠X = _____˚

m∠Y = _____˚

m∠Z = _____˚

Segment AB = _____ units

Segment BC = _____ units

Segment AC = _____ units

Segment XY = _____ units

Segment YZ = _____ units

Segment XZ = _____ units

Answer 1

Given:

Two triangles are congruent, i.e.,
`\Delta ABC\cong \Delta XYZ`.

To find:

All the measures of both triangle.

Solution:

We have,

`\Delta ABC\cong \Delta XYZ`.

We know that, corresponding parts of congruent triangles are congruent (CPCTC).

`\angle A=\angle X`

`\angle B=\angle Y=90^\circ`

`\angle C=\angle Z=37^\circ`

It triangle ABC,

`\angle A+\angle B+\angle C=180^\circ` (Angle sum property)

`\angle A+90^\circ+37^\circ=180^\circ`

`\angle A+127^\circ=180^\circ`

`\angle A=180^\circ -127^\circ`

`\angle A=53^\circ`

So,

`\angle A=\angle C=53^\circ`

`AB=XY=3\text{ units}`

`BC=YZ=4\text{ units}`

`AC=XZ=5\text{ units}`

Therefore, m∠A = 53˚, m∠B =90˚ , m∠C =37˚ , m∠X = 53˚, m∠Y =90˚ , m∠Z =37˚ , Segment AB = 3 units , Segment BC = 4 units , Segment AC = 5 units , Segment XY = 3 units , Segment YZ = 4 units , Segment XZ = 5 units .