Question 1

You are an architect designing triangular steel supports for a building. You need to ensure that the supports are congruent so they will fit perfectly and provide the necessary strength. You are given the following measurements for two triangular supports:

• Support 1: Side AB=6m, Side BC=8m and ∠ABC=45∘

• Support 2: Side DE=6m, Side EF=8 m, and ∠DEF=45∘

You need to determine whether the two triangular supports are congruent based on the SAS Postulate.

1. Based on themeasurements provided for Support 1 and Support 2, which postulate can be usedto prove that the two supports are congruent?

Accepted Answer

Side-Angle-Side (SAS) Postulate

Answer

Angle-Side-Angle (ASA)Postulate

Answer

Angle-Angle-Angle (AAA) Postulate

Answer

Side-Side-Side(SSS) Postulate

Question 2

You are an architect designing triangular steel supports for a building. You need to ensure that the supports are congruent so they will fit perfectly and provide the necessary strength. You are given the following measurements for two triangular supports:

• Support 1: Side AB=6m, Side BC=8m and ∠ABC=45∘

• Support 2: Side DE=6m, Side EF=8 m, and ∠DEF=45∘

You need to determine whether the two triangular supports are congruent based on the SAS Postulate.

2. What is the key condition that must be met for the two triangles to be congruent based on the SAS Postulate?

Accepted Answer

Two sides must be equal, and the included angle must be the same between the sides.

Answer

All three angles must be equal.

Answer

All three sides must be equal.

Answer

Both triangles must have equal angles and equal side lengths.

Question 3

You are an architect designing triangular steel supports for a building. You need to ensure that the supports are congruent so they will fit perfectly and provide the necessary strength. You are given the following measurements for two triangular supports:

• Support 1: Side AB=6m, Side BC=8m and ∠ABC=45∘

• Support 2: Side DE=6m, Side EF=8 m, and ∠DEF=45∘

You need to determine whether the two triangular supports are congruent based on the SAS Postulate.

3. If the angle between sides AB and BC in Support 1 were changed to 60∘, what would happen to the congruence of the triangles?

Accepted Answer

The triangles would no longer be congruent because the included angle is different.

Answer

The triangles would still be congruent because the sides are equal.

Answer

The triangles would no longer be congruent because the sides are different.

Answer

The triangles would still be congruent because the angles are not important.

Question 4

You are an architect designing triangular steel supports for a building. You need to ensure that the supports are congruent so they will fit perfectly and provide the necessary strength. You are given the following measurements for two triangular supports:

• Support 1: Side AB=6m, Side BC=8m and ∠ABC=45∘

• Support 2: Side DE=6m, Side EF=8 m, and ∠DEF=45∘

You need to determine whether the two triangular supports are congruent based on the SAS Postulate.

4. If you wanted to test the congruence of two triangular supports, which of the following methods would you use based on the SAS Postulate?

Accepted Answer

Measure two sides and the included angle in both triangles and check for equality.

Answer

Measure all angles in both triangles and compare them.

Answer

Compare the perimeter of both triangles.

Answer

Measure the area of both triangles and compare the values.

Question 5

You are an architect designing triangular steel supports for a building. You need to ensure that the supports are congruent so they will fit perfectly and provide the necessary strength. You are given the following measurements for two triangular supports:

• Support 1: Side AB=6m, Side BC=8m and ∠ABC=45∘

• Support 2: Side DE=6m, Side EF=8 m, and ∠DEF=45∘

You need to determine whether the two triangular supports are congruent based on the SAS Postulate.

5. Why is it important to ensure that the supports in the design are congruent?

Accepted Answer

To make sure the supports are exactly the same shape and size, ensuring they fit perfectly and are strong.

Answer

To ensure that the building is aesthetically pleasing.

Answer

To reduce the number of materials used in the design.

Answer

To make sure the angles are more than 90°.

Question 6

Refer to the situation below Here you see a photograph of a farmhouse with a roof in the shape of a pyramid. Next to it is a student's mathematical model of the farmhouse roof with measurements added.The attic floor, ABCD in the model, is a square. that support the roof are the edges of a block(rectangular prism) EFGHKLMN.Eis the middle of ATFis the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12m.

6. Triangles TAD and TCD are other faces of the pyramid roof. The lengths of their sides are shown on student’s mathematical model.

Which of the following statements is true?

6. Triangles TAD and TCD are other faces of the pyramid roof. The lengths of their sides are shown on student’s mathematical model.

Which of the following statements is true?

Accepted Answer

Triangles TAD and TCD are congruent because the corresponding sides are equal.

Answer

Triangles TAD and TCD are not congruent because their sides aredifferent in length.

Answer

Triangles TAD and TCD are congruent because their angles are equal.

Answer

Triangles TAD and TCD are not congruent because only one pair of sides is equal.

Question 7

Refer to this situation for items 7 and 8

You are a carpenter tasked with cutting two identical triangular pieces of wood for a set of shelves. The side lengths of the triangles are fixed as follows:

Side 1 = 12 inches, Side 2 = 15 inches, Side 3 = 18 inches.

You need to verify whether your two pieces of wood are congruent

7. How can you be sure that the two triangular pieces of wood are congruent?

Accepted Answer

If the two pieces have matching side lengths of 12 inches, 15 inches, and 18 inches, they will be congruent, no further checks are needed.

Answer

If the two pieces have matching angles, they are congruent.

Answer

If the two pieces have the same area, they are congruent.

Answer

If the pieces have the same perimeter, they must be congruent.

Question 8

Refer to this situation for items 7 and 8

You are a carpenter tasked with cutting two identical triangular pieces of wood for a set of shelves. The side lengths of the triangles are fixed as follows:

Side 1 = 12 inches, Side 2 = 15 inches, Side 3 = 18 inches.

You need to verify whether your two pieces of wood are congruent

8. Whichof the following methods should you use to ensure that the two triangularpieces of wood are congruent

Accepted Answer

Check that the two triangles have the same perimeter. If the perimeter is the same,the triangles must be congruent.

Answer

Measure the angles of the two triangles. If the angles are identical, the triangles are congruent.

Answer

Compare the three side lengths of each triangle. If all three sides of one triangle match the corresponding sides of the other triangle, the triangles are congruent.

Answer

Compare the areas of the two triangles. If the areas are the same,the triangles must be congruent.

Question 9

A triangular window pane has sides AB=4m , BC=3m, and AC=5m. The designer wants to create a second congruent triangles.

What are the lemgths of the corresponding sides in the second triamgle?

Accepted Answer

AB = 4m, BC=3m, and AC=5m

Answer

AB= 3m, BC=4m, and AC=5m

Answer

AB=4m, BC=5m, and AC=3m

Answer

AB= 5m, BC=3m, and AC=4m

Question 10

Two congruent triangles, △ABC and △DEF, are given.

△ABC has ∠A=40∘,∠B=60∘,∠C=80∘. List the corresponding angles in △DEF.

Accepted Answer

∠A↔∠D, ∠B↔∠E, ∠C↔∠F

Answer

∠A↔∠F, ∠B↔∠D, ∠C↔∠E

Answer

∠A↔∠C, ∠B↔∠E, ∠C↔∠F

Answer

∠A↔∠B, ∠C↔∠D, ∠E↔∠F

Question 11

Two congruent triangles, △ABC and △DEF, are used in a design. ∠A=45∘, ∠B=55∘

What is the measure of ∠C in △ABC?

Accepted Answer

∠C = 80°

Answer

∠C = 90°

Answer

∠C = 75°

Answer

∠C = 95°

Question 12

Two congruent triangles, △ABC and △DEF, are used in a design. ∠A=45∘, ∠B=55∘

What are the corresponding angle measures in △ABC?What are the corresponding angle measures in △ABC?

Accepted Answer

∠A=45∘,∠B=55∘,∠C=80∘

Answer

∠A=45∘,∠B=80∘,∠C=55∘

Answer

∠A=55∘,∠B=45∘,∠C=80∘

Answer

∠A=80∘,∠B=55∘,∠C=45∘

Question 13

Refer to the picture below.

Accepted Answer

https://uploads.quizalize.com/37ca6001-66a4-4933-8cde-297ba0012870/question/1e2c8db03984dfb01d9edec598966dfa27cc8eb3.jpeg

Answer

https://uploads.quizalize.com/37ca6001-66a4-4933-8cde-297ba0012870/question/d79e3764ffc42ec18c34a505ddca886259af8f90.jpeg

Answer

https://uploads.quizalize.com/37ca6001-66a4-4933-8cde-297ba0012870/question/dc459992a8e3b6100cb3286e11f7ae8e0080d9e2.jpeg

Answer

https://uploads.quizalize.com/37ca6001-66a4-4933-8cde-297ba0012870/question/3eeb6488454840ccc4a8bc0045f658c66b812c9d.jpeg

Question 14

Which of the following statements is not sufficient to prove the congruence of two triangles?Which of the following statements is not sufficient to prove the congruence of two triangles?

Accepted Answer

Two sides of one triangle are congruent respectively to the two sides of another triangle.

Answer

Two angles and the non–included side of one triangle are congruent respectively to the two angles and the non–included side of another triangle.

Answer

Two angles and the included side of one triangle are congruent respectively to the two angles and the included side of another triangle.

Answer

Three sides of one triangle are congruent respectively to the three sides of another triangle.

Question 15

Which of the following is the congruence statement of

the two triangles as illustrated on the right?

Accepted Answer

△ABC ≌ △ZYX

Answer

△CBA ≌ △XZY

Answer

△CBA ≌ △ZYX

Answer

△ABC ≌ △XYZ

Question 16

A truss is a triangulated structure that consists of straight structural components like beams, bars, or rods joined together. This is used in supporting construction such as bridges, buildings, and other infrastructure that needs a sturdy framework. As shown in the figure at the right, what congruence postulate is illustrated as △MAH ≌ △TAH?

Accepted Answer

SAS Congruence Postulate

Answer

SSS Congruence Postulate

Answer

ASA Congruence Postulate

Answer

AAS Theorem

Question 17

Refer to the picture.

Accepted Answer

true

Answer

false

Question 18

Which of the following reasons associates △FSD with △LDS?

Accepted Answer

Right Angle Triangle Theorem

Answer

Reflexive Property of Congruence

Answer

Definition of Perpendicular Lines

Answer

<P>Given</P>

Question 19

The Buntun Bridge is one of the longest river bridges in the Philippines. At 1,098 meters in length, it was first opened to the public in 1947. It is often referred to as Tuguegarao City’s gateway. Although the river has never flooded the bridge, typhoons Ondoy and Juan almost did. Its structures, consisting of congruent triangles, are among the reasons it remains firm even today.