Congruent Triangles 2
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Question 1 of 3
1. Question
Is `∆XWY` congruent to `∆WYZ`
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `/_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 `\text((RHS))` criteriaYes, `∆XWY` is congruent to `∆WYZ`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side `\text((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 `\text((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 `\text((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 TypesAlternate 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
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Question 2 of 3
2. Question
Is `∆STR` congruent to `∆PTQ`
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruent
Statement: `SR``=``PQ`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 `\text((AAS))` criteriaYes, `∆STR` is congruent to `∆PTQ`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.Side-Angle-Side `\text((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 otherAngle-Angle-Side `\text((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 `\text((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 anotherAlternate, Corresponding and Co-Interior Angle TypesAlternate 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 -
Question 3 of 3
3. Question
Is side `JK` equal to side `HL`
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `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 `\text((SAS))` criteriaSince 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 InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.Side-Angle-Side `\text((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 otherAngle-Angle-Side `\text((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 `\text((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 anotherAlternate, Corresponding and Co-Interior Angle TypesAlternate 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