Summative Test (Pisa-like)
Quiz by DiCNHS Math Dept.
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- Q1
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?
Angle-Side-Angle (ASA)Postulate
Angle-Angle-Angle (AAA) Postulate
Side-Angle-Side (SAS) Postulate
Side-Side-Side(SSS) Postulate
60s - Q2
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?
All three angles must be equal.
Two sides must be equal, and the included angle must be the same between the sides.
All three sides must be equal.
Both triangles must have equal angles and equal side lengths.
30s - Q3
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?
The triangles would still be congruent because the sides are equal.
The triangles would no longer be congruent because the included angle is different.
The triangles would no longer be congruent because the sides are different.
The triangles would still be congruent because the angles are not important.
30s - Q4
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?
Measure two sides and the included angle in both triangles and check for equality.
Measure all angles in both triangles and compare them.
Compare the perimeter of both triangles.
Measure the area of both triangles and compare the values.
30s - Q5
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?
To ensure that the building is aesthetically pleasing.
To reduce the number of materials used in the design.
To make sure the angles are more than 90°.
To make sure the supports are exactly the same shape and size, ensuring they fit perfectly and are strong.
30s - Q6
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?
Triangles TAD and TCD are not congruent because their sides aredifferent in length.
Triangles TAD and TCD are congruent because their angles are equal.
Triangles TAD and TCD are congruent because the corresponding sides are equal.
Triangles TAD and TCD are not congruent because only one pair of sides is equal.
30s - Q7
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 congruent7. How can you be sure that the two triangular pieces of wood are congruent?
If the two pieces have matching angles, they are congruent.
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.
If the two pieces have the same area, they are congruent.
If the pieces have the same perimeter, they must be congruent.
30s - Q8
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
Measure the angles of the two triangles. If the angles are identical, the triangles are congruent.
Check that the two triangles have the same perimeter. If the perimeter is the same,the triangles must be congruent.
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.
Compare the areas of the two triangles. If the areas are the same,the triangles must be congruent.
30s - Q9
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?
AB= 3m, BC=4m, and AC=5m
AB=4m, BC=5m, and AC=3m
AB = 4m, BC=3m, and AC=5m
AB= 5m, BC=3m, and AC=4m
30s - Q10
Two congruent triangles, △ABC and △DEF, are given.
△ABC has ∠A=40∘,∠B=60∘,∠C=80∘. List the corresponding angles in △DEF.
∠A↔∠F, ∠B↔∠D, ∠C↔∠E
∠A↔∠D, ∠B↔∠E, ∠C↔∠F
∠A↔∠C, ∠B↔∠E, ∠C↔∠F
∠A↔∠B, ∠C↔∠D, ∠E↔∠F
30s - Q11
Two congruent triangles, △ABC and △DEF, are used in a design. ∠A=45∘, ∠B=55∘
What is the measure of ∠C in △ABC?
∠C = 90°
∠C = 75°
∠C = 95°
∠C = 80°
30s - Q12
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?
∠A=45∘,∠B=80∘,∠C=55∘
∠A=55∘,∠B=45∘,∠C=80∘
∠A=80∘,∠B=55∘,∠C=45∘
∠A=45∘,∠B=55∘,∠C=80∘
30s - Q13
Refer to the picture below.
30s - Q14
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?
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.
Two angles and the included side of one triangle are congruent respectively to the two angles and the included side of another triangle.
Three sides of one triangle are congruent respectively to the three sides of another triangle.
Two sides of one triangle are congruent respectively to the two sides of another triangle.
30s - Q15
Which of the following is the congruence statement of
the two triangles as illustrated on the right?
△ABC ≌ △ZYX
△CBA ≌ △XZY
△CBA ≌ △ZYX
△ABC ≌ △XYZ
30s
