Congruent Triangles Quiz

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Questions and Answers

Given ∆ABC ≅ ∆DEF, if m∠B = 65°, m∠C= 42°, and m∠A=73°, what is the measure of ∠E?

  • 65° (correct)
  • 42°
  • 180°
  • 73°

Given ∆ABC ≅ ∆DEF, if DE = 2.6 cm, EF = 3.7 cm, and CA = 3.5 cm, what is the length of the side BC?

  • 2.6 cm
  • Cannot be determined
  • 3.7 cm (correct)
  • 3.5 cm

If ∆PQR ≅ ∆XYZ, and PQ = 5x + 2 and XY = 7x - 6, find the value of x.

  • 2
  • 6
  • 4 (correct)
  • 8

If ∆ABC ≅ ∆LMN and ∠A = 90°, ∠B = 30°, what is the measure of ∠N?

<p>60° (B)</p> Signup and view all the answers

If ∆RST ≅ ∆UVW, and RS = 3a - 5 and UV = 2a + 1, what is the length of RS?

<p>13 (A)</p> Signup and view all the answers

Given ∆ABC ≅ ∆XYZ, where AC = 5y, XZ = 3y+8, What is the value of y?

<p>4 (A)</p> Signup and view all the answers

Given ∆PQR ≅ ∆STU, ∠P = 2b +3, ∠S = 5b -9, what the measure of ∠P?

<p>11 (C)</p> Signup and view all the answers

If ∆ABC ≅ ∆DEF, and AB = 6, BC = 8, and AC = 10, what is the perimeter of ∆DEF?

<p>24 (C)</p> Signup and view all the answers

If two triangles are congruent, which of the following statements is always true about their corresponding parts?

<p>Corresponding sides are congruent, and corresponding angles are congruent. (C)</p> Signup and view all the answers

What does CPCTC stand for, and how is it used in geometry?

<p>Corresponding Parts of Congruent Triangles are Congruent; used to prove equality of parts in congruent triangles. (B)</p> Signup and view all the answers

Given two triangles, LMN and PQR, are congruent (LMN PQR), and it is known that side LM corresponds with side PQ and side MN corresponds with side QR, with L = 50 and N = 70, what is the measure of R?

<p>70 (B)</p> Signup and view all the answers

If ABC DEF, and the length of AB is 8cm, and EF is 10cm, and AC is 12cm, what is the length of DE?

<p>8cm (D)</p> Signup and view all the answers

Which of the following is NOT a corresponding part of congruent triangles?

<p>Corresponding perimeters (A)</p> Signup and view all the answers

In two congruent triangles, if one angle in the first triangle measures $90^{\circ}$ and another angle measures $30^{\circ}$, what must be the measure of the corresponding angles in the second triangle?

<p>$30^{\circ}$ and $90^{\circ}$ (A)</p> Signup and view all the answers

Given ABC XYZ, which of the following statements is true?

<p>Side BC corresponds to side YZ (A)</p> Signup and view all the answers

Two triangles, RST and UVW, are congruent. If RS = 5cm, ST = 7cm, and RT = 9cm, what are the lengths of corresponding sides of UVW?

<p>UV = 5cm, VW = 7cm, UW = 9cm (A)</p> Signup and view all the answers

Given that ∆PQR ≅ ∆STU, what does the statement ∠Q ≅ ∠T imply about the respective vertices?

<p>Vertex Q corresponds to vertex T. (C)</p> Signup and view all the answers

If ∆LMN ≅ ∆XYZ, and segment LM measures 5 cm, which side of ∆XYZ also measures 5 cm?

<p>Segment XY (B)</p> Signup and view all the answers

Given ∆ABC ≅ ∆DEF, which of the following statements is NOT necessarily true?

<p>∠B ≅ ∠F (C)</p> Signup and view all the answers

If ∆RST ≅ ∆UVW and m∠R = 60°, and m∠U = 70°, what is the measure of ∠V?

<p>60° (B)</p> Signup and view all the answers

Consider two congruent triangles ∆ABC and ∆LMN. If it is known that AB ≅ LM, and BC ≅ MN, what part of triangle ∆LMN is congruent to AC?

<p>LN (C)</p> Signup and view all the answers

Given ∆XYZ ≅ ∆PQR, if XY = 8cm, XZ = 10cm and YZ = 12cm, and PQ = 8cm, what is the measure of PR?

<p>10cm (B)</p> Signup and view all the answers

Given ∆DEF ≅ ∆GHI, which statement is correct if ∠D = 50°, ∠E = 70° and the side corresponding to side EF has a length of 12cm. Which of the following is true?

<p>∠I = 70° and HI = 12cm (A)</p> Signup and view all the answers

In congruent triangles ∆ABC and ∆XYZ, if AB corresponds to XY, BC corresponds to YZ, and AC corresponds to XZ, which angle is congruent to ∠B?

<p>∠Y (C)</p> Signup and view all the answers

Flashcards

Congruent Triangles Definition

Two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.

Corresponding Sides

Sides of congruent triangles that correspond to each other.

Corresponding Angles

Angles of congruent triangles that correspond to each other.

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

When all corresponding parts of two triangles are congruent, the triangles are congruent.

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Vertices of a Triangle

The points where the sides of a triangle meet.

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Correspondence (Triangles)

Describes how the parts of two triangles are connected.

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Measure (Side/Angle)

The measure of a side or an angle of a triangle.

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Solving Corresponding Parts

To find the measure of one of the corresponding parts of a congruent triangle.

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Corresponding Angles in Congruent Triangles

Corresponding angles in congruent triangles are equal in measure.

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Corresponding Sides in Congruent Triangles

Corresponding sides in congruent triangles are equal in length.

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CPCTC

The Corresponding Parts of Congruent Triangles are Congruent (CPCTC) states that if two triangles are congruent, then all corresponding parts (angles and sides) are also congruent.

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Finding Unknown Values in Congruent Triangles

To determine the value of an unknown in congruent triangles, use the fact that corresponding sides and angles are congruent.

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How to Find Missing Values in Congruent Triangles

To find the value of a missing angle or side in a congruent triangle, you can use the principle of Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

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Identifying Corresponding Vertices

When identifying corresponding vertices in congruent triangles, use the order of the letters in the triangle names to match the corresponding angles and sides.

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Solving for Variables in Congruent Triangles

To find the value of a variable in a congruent triangle, substitute the given measurements into the expressions for the corresponding sides and solve the equation.

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Substitution Method in Congruent Triangles

The Substitution Method involves replacing a variable with a given equivalent expression to solve for its value.

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Congruent Triangles

Triangles that have the same shape and size. Every corresponding angle and side of these triangles are equal.

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What is the first step in solving for the missing parts of congruent triangles?

To identify corresponding angles and sides of congruent triangles.

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What is the second step in solving for the missing parts of congruent triangles?

List the corresponding angles and sides to identify which parts are congruent.

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Why is understanding corresponding parts of congruent triangles important?

Understanding corresponding angles and sides of congruent triangles is essential for solving problems in Geometry.

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How does CPCTC help us solve for missing parts?

CPCTC allows us to use known information about one triangle to determine missing information about its congruent counterpart.

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Study Notes

Congruent Triangles

  • Congruent triangles have corresponding sides and angles that are equal in measure.
  • Corresponding parts of congruent triangles are congruent. (CPCTC)

Solving Corresponding Parts of Congruent Triangles

  • Given congruent triangles, find the missing parts by identifying corresponding parts.
  • Write corresponding vertices, angles and sides.
  • Use CPCTC to solve for unknown values
  • Substitute values into equations, and solve for unknown variables (x or y).
  • Find the missing angles and sides.
  • Match corresponding sides and angles.

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