Use the given diagram to determine whether any of the angles or sides are congruent
Statement: ∠XYW=∠WYZ
Reason: Since ∠WYZ=90° and the two angles lie on a straight line, they have a sum of 180°
(R) Right Angle
Statement: XW=ZW
Reason: Given by the markings (one dash) on each segment
(H) Hypotenuse
Statement: WY=WY
Reason: This is a common side for both triangles
(S) Side
We have proved congruence of a right angle, the hypotenuse, and 1 side between the two triangles. Therefore, the two triangles are congruent according to the Right Angle-Hypotenuse-Side (RHS) criteria
Yes, ΔXWY is congruent to ΔWYZ
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Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°. These angles typically form a C Shape
Reason: Opposite sides of a parallelogram are equal.
(S) Side
We have proved congruence of 1 side and 2 angles between the two triangles. Therefore, the two triangles are congruent according to the Angle-Angle-Side (AAS) criteria
Yes, ΔSTR is congruent to ΔPTQ
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Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°. These angles typically form a C Shape
Use the given diagram to determine whether any of the angles or sides are congruent
Statement: GK=LI
Reason: Given by the markings (two dashes) on each segment
(S) Side
Statement: ∠KGJ=∠HIL
Reason: Opposite angles of a parallelogram are equal.
(A) Angle
Statement: GJ=HI
Reason: Opposite sides of a parallelogram are equal.
(S) Side
We have proved congruence of 2 sides and 1 angle between the two triangles. Therefore, the two triangles are congruent according to the Side-Angle-Side (SAS) criteria
Since we have proven the congruence of the two triangles, it means that corresponding sides, such as sides JK and HL, are equal.
Yes, side JK is equal to side HL
More Info
Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°. These angles typically form a C Shape