Question

!50 POINTS! (4 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
|
|
\/

Answer 1

1st question: e. SSS

2nd question: b. SAS

3rd question: b. Δ JLK

4th question: e. SAS

Explanation:

Note: Following condition should need to be fulfilled to be congruent triangle:

• SSS (Side-Side-Side): If the three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent.
• SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent.
• ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the two triangles are congruent.
• AAS (Angle-Angle-Side): If two angles and any side of one triangle are equal to the corresponding two angles and the same side of another triangle, then the two triangles are congruent.
• RHS (Right-Angle-Hypotenuse-Side): If one triangle is a right triangle and the hypotenuse and one leg are equal to the hypotenuse and the corresponding leg of another right triangle, then the two triangles are congruent.

`\hrulefill`

For 1st Question:

In Δ PQR and ΔSTU
PQ=ST side

PR=SU side

QR=TU side

Therefore, Δ PQR ≅ ΔSTU By SSS axiom.

So, the answer is e. SSS

`\hrulefill`

For 2nd question:

In ΔSTR and Δ PQR

TR=PR side

m ∡ SRT = m ∡ PRQ Vertically opposite angle
SR=QR side

Therefore, Δ STR ≅ ΔPQR By SAS axiom.

So, the answer is b. SAS

`\hrulefill`

For 3rd Question:

In Δ QPR and Δ JLK

PR=LK side

m ∡ PRQ = m ∡ JKL Given Angle

QR=JK side

Therefore, Δ QPR ≅ Δ JLK By SAS axiom.

We can named the name of triangle by comparing congruent side and angle of the triangle

So, the answer is b. Δ JLK

`\hrulefill`

For 4th Question:

In Δ QPR and Δ JLK

PR=LK side

m ∡ PRQ = m ∡ JKL Given Angle

QR=JK side

Therefore, Δ QPR ≅ Δ JLK By SAS axiom.

So, the answer is e. SAS