4.4.7

Congruent Triangles

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Congruent Triangles

Two shapes are congruent if they are the same shape and same size. They can be rotations or reflections of each other. There are four ways to prove two triangles are congruent:

SSS (side, side, side)

SSS (side, side, side)

  • The three sides must be the same lengths.
SAS (side, angle, side)

SAS (side, angle, side)

  • Two sides and the angle between them must be the same.
ASA (angle, side, angle)

ASA (angle, side, angle)

  • Two angles and the side between them must be the same.
RHS (right angle, hypotenuse, side)

RHS (right angle, hypotenuse, side)

  • There must be a right angle in both triangles and the hypotenuse and one other side must be the same lengths.
Jump to other topics
1

Number

1.1

Place Value

1.1.1Ordering Numbers1.1.2Ordering Numbers - Practice1.1.3Comparing Numbers1.1.4Comparing Numbers - Practice1.1.5Equals Symbols1.1.6Equals Symbols - Practice1.1.7Adding Negative Numbers1.1.8Adding Negative Numbers - Practice1.1.9Subtracting Negative Numbers1.1.10Multiplying Negative Numbers1.1.11Dividing Negative Numbers1.1.12End of Topic Test - Place Value
1.2

Factors & Multiples

1.2.1Factors1.2.2Factors - Practice1.2.3Prime Numbers1.2.4Prime Numbers - Practice1.2.5Multiples1.2.6Multiples - Practice1.2.7Prime Factors1.2.8Prime Factors - Practice1.2.9Highest Common Factors1.2.10Highest Common Factors - Practice1.2.11Highest Common Factor Prime Factors1.2.12Highest Common Factor Prime Factors - Practice1.2.13Lowest Common Multiples1.2.14Lowest Common Multiples - Practice1.2.15Lowest Common Multiples Prime Factors1.2.16Lowest Common Multiples Prime Factors - Practice1.2.17End of Topic Test - Factors & Multiples
1.3

Operations

1.3.1Addition1.3.2Addition - Practice1.3.3Subtraction1.3.4Subtraction - Practice1.3.5Multiplication 10,100...1.3.6Multiplication 10,100... - Practice1.3.7Grid Multiplication1.3.8Grid Multiplication - Practice1.3.9Division by 10s1.3.10Division by 10s - Practice1.3.11Powers1.3.12Powers - Practice1.3.13Roots1.3.14Roots - Practice1.3.15Surds1.3.16Surds - Practice1.3.17Rationalise denominator1.3.18Rationalise Denominator - Practice1.3.19Simplify Surds1.3.20Simplify Surds - Practice1.3.21BIDMAS1.3.22BIDMAS - Practice1.3.23Inverse Ops1.3.24Inverse Ops - Practice1.3.25Standard Form1.3.26Addition in Standard Form1.3.27Subtraction in Standard Form1.3.28End of Topic Test - Operations1.3.29End of Topic Test - Standard Form
1.4

Fractions, Decimals & Percentages

1.4.1Fractions1.4.2Fractions - Practice1.4.3Mixed & Improper Fractions1.4.4Mixed & Improper Fractions - Practice1.4.5Write 2 Numbers as Fractions1.4.6Write 2 Numbers as Fractions - Practice1.4.7Adding Fractions1.4.8Adding Fractions - Practice1.4.9Subtracting Fractions1.4.10Multiplying Fractions1.4.11Multiplying Fractions - Practice1.4.12Dividing Fractions1.4.13Finding Fractions1.4.14Finding Fractions - Practice1.4.15Improper & Mixed Fractions1.4.16Decimal Place Value1.4.17Decimal Place Value - Practice1.4.18Fraction to Decimal1.4.19Fraction to Decimal - Practice1.4.20Find Percentage Unitary1.4.21Find Percentage Unitary - Practice1.4.22Fraction to Percentage1.4.23Fraction to Percentage - Practice1.4.24Percentage to Fraction1.4.25Percentage to Decimal1.4.26Percentage to Decimal - Practice1.4.27Decimal to Percentage1.4.28Decimal to Percentage - Practice1.4.29Percentage using Decimal1.4.30End of Topic Test - Fractions1.4.31End of Topic Test - Decimals
1.5

Growth & Decay

1.5.1Population Growth1.5.2Population Growth - Practice1.5.3Compound Growth & Decay1.5.4Compound Growth & Decay - Practice1.5.5Compound Interest1.5.6Compound Interest - Practice1.5.7Compound Interest 21.5.8Compound Interest 2 - Practice1.5.9Depreciation1.5.10Depreciation - Practice1.5.11End of Topic Test - Growth & Decay
1.6

Measurements & Units

1.6.1Standard Units 11.6.2Standard Units 1 - Practice1.6.3Standard Units 21.6.4Standard Units 2 - Practice1.6.5Standard Units 31.6.6Standard Units 3 - Practice1.6.7Length1.6.8Area1.6.9Volume1.6.10Capacity1.6.11Time1.6.12Time - Practice1.6.13Money1.6.14Mass1.6.15End of Topic Test - Measurements & Units
1.7

Accuracy

1.7.1Decimal Rounding1.7.2Decimal Rounding - Practice1.7.3SigFig Rounding1.7.4SigFig Rounding - Practice1.7.5Estimations1.7.6Estimations - Practice1.7.7Upper Lower Bounds1.7.8Upper Lower Bounds - Practice1.7.9End of Topic Test - Accuracy
2

Algebra

2.1

Introduction to Algebra

2.1.1Algebra Basics2.1.2Algebra Basics - Practice2.1.3Algebraic Concepts2.1.4Algebraic Concepts - Practice2.1.5Writing Expressions2.1.6Writing Expressions - Practice2.1.7Collecting Terms2.1.8Collecting Terms - Practice2.1.9Common Factors2.1.10Common Factors - Practice2.1.11Expanding Brackets2.1.12Expanding Brackets - Practice2.1.13FOIL2.1.14FOIL - Practice2.1.15Rearranging Formulae2.1.16Rearranging Formulae - Practice2.1.17End of Topic Test - Introduction to Algebra
2.2

Graphs

2.2.1Coordinates2.2.2Coordinates - Practice2.2.3Gradient and Intercept2.2.4Gradient and Intercept - Practice2.2.5Calculate Gradient &Y-intercept2.2.6Calculate Gradient & Y-intercept2.2.7Finding Equation2.2.8Finding Equation - Practice2.2.9Quadratic Graphs2.2.10Quadratic Graphs - Practice2.2.11End of Topic Test - Graphs
2.3

Solving Equations

2.3.1Solve Linear Equations2.3.2Solve Linear Equations - Practice2.3.3Words To Equation2.3.4Words To Equation - Practice2.3.5Solve Linear Equations Graphically2.3.6Solve Linear Equations Graphically - Practice2.3.7Solve Inequality2.3.8Solve Inequality - Practice2.3.9Graphing Inequalities2.3.10Graphing Inequalities - Practice2.3.11Simultaneous Equations2.3.12Simultaneous Equations - Practice2.3.13Simultaneous Equations Graph2.3.14Simultaneous Equations Graph - Practice2.3.15Quadratic +/-2.3.16Quadratic +/- - Practice2.3.17Factorise Quadratics2.3.18Factorise Quadratics - Practice2.3.19Complete the Square2.3.20Complete the Square - Practice2.3.21End of Topic Test - Graphs & Equations2.3.22End of Topic Test - Solving Equations
2.4

Sequences

2.4.1Arith & Geo Sequences2.4.2Arith & Geo Sequences - Practice2.4.3Key Sequences2.4.4Key Sequences - Practice2.4.5Nth Term Rules2.4.6Nth Term Rules - Practice2.4.7Find NthTerm in Linear Sequence2.4.8Find NthTerm in Linear Sequence - Practice2.4.9Find Nth Term in Quadratic Sequence2.4.10Find Nth Term in Quadratic Sequence - Practice2.4.11End of Topic Test - Sequences
3

Ratio, Proportion & Rates of Change

3.1

Manipulating Ratios

3.1.1Manipulating Ratios3.1.2Manipulating Ratios - Practice3.1.3Turn Ratios into Equations3.1.4Turn Ratios into Equations - Practice3.1.5Part:Part Ratio3.1.6Part:Part Ratio - Practice3.1.7Part:Whole Ratio3.1.8Part:Whole Ratio - Practice3.1.9Differences in Ratios3.1.10Differences in Ratios - Practice3.1.11Fractions in Ratios3.1.12Fractions in Ratios - Practice3.1.13Ratios to Fractions3.1.14Ratios to Fractions - Practice3.1.15End of Topic Test - Manipulating Ratios
3.2

Ratios in Practice

3.2.1Covert Units3.2.2Covert Units - Practice3.2.3Formula Triangles3.2.4Formula Triangles - Practice3.2.5Scale Factors3.2.6Scale Factors - Practice3.2.7Ratios in Shapes3.2.8Ratios in Shapes - Practice3.2.9End of Topic Test - Ratios
3.3

Percentage & Finance

3.3.1Percentage Increase/Decrease3.3.2Percentage Increase/Decrease - Practice3.3.3Percentage Change3.3.4Percentage Change - Practice3.3.5Original Value3.3.6Original Value - Practice3.3.7Profit, Interest & Discount3.3.8Profit, Interest & Discount - Practice3.3.9Simple Interest3.3.10Simple Interest - Practice3.3.11End of Topic Test - Percentage & Finance
3.4

Proportion

3.4.1Proportion3.4.2Proportion - Practice3.4.3Direct Proportion3.4.4Direct Proportion - Practice3.4.5Inverse Proportion3.4.6Inverse Proportion - Practice3.4.7End of Topic Test - Percentages & Proportion
4

Geometry & Measures

4.1

Introduction to Geometry

4.1.1LinesAngles14.1.2LinesAngles1 - Practice4.1.3LinesAngles24.1.4LinesAngles2 - Practice4.1.5Regular Polygons4.1.6Regular Polygons - Practice4.1.7Triangles and Angles4.1.8Triangles and Angles - Practice4.1.9Quadrilaterals4.1.10Quadrilaterals - Practice4.1.11Midpoints4.1.12Midpoints - Practice4.1.13Bisectors and Perpendiculars4.1.14Bisectors and Perpendiculars - Practice4.1.15Angle Rules4.1.16Angle Rules - Practice4.1.17Angles in Parallel Lines4.1.18Angles in Parallel Lines - Practice4.1.19Angles in a Polygon4.1.20Angles in a Polygon - Practice4.1.21Angles in a Triangle4.1.22Angles in a Triangle - Practice4.1.23Bearings4.1.24Bearings - Practice4.1.25End of Topic Test - Geometry4.1.26End of Topic Test - Geometry & Measures
4.2

Ruler & Compass Constructions

4.2.1Midpoint4.2.2Bisectors and Perpendiculars4.2.3Loci4.2.4End of Topic Test - Ruler & Compass Constructions
4.3

Perimeter & Area

4.3.1Perimeter4.3.2Perimeter - Practice4.3.3Area4.3.4Area - Practice4.3.5End of Topic Test - Perimeter & Area
4.4

Triangles, Quadrilaterals & Circles

4.4.1Types of Triangle4.4.2Types of Triangle - Practice4.4.3Angles & Triangles4.4.4Angles & Triangles - Practice4.4.5Congruence4.4.6Congruence - Practice4.4.7Congruent Triangles4.4.8Congruent Triangles - Practice4.4.9Similar Triangles4.4.10Similar Triangles - Practice4.4.11Scale Factors & Enlargement4.4.12Scale Factors & Enlargement - Practice4.4.13Properties of Circle 14.4.14Properties of Circle 1 - Practice4.4.15Properties of a Circle 24.4.16Properties of a Circle 2 - Practice4.4.17Area of a Circle4.4.18Area of a Circle - Practice4.4.19Circumference of a Circle4.4.20End of Topic Test - Triangles, Quadrilaterals4.4.21End of Topic Test - Circles
4.5

Transformations

4.5.1Types of Transformations4.5.2Types of Transformations - Practice4.5.3Effects of Transformations4.5.4Effects of Transformations - Practice4.5.5End of Topic Test - Transformations
4.6

Triangle Formulae

4.6.1Pythagoras' Theorem4.6.2Pythagoras' Theorem - Practice4.6.3Trigonometric Ratios4.6.4Trigonometric Ratios - Practice4.6.5End of Topic Test - Triangle Formulae
4.7

3D Shapes

4.7.1Types of 3D Shape4.7.2Types of 3D Shape - Practice4.7.3Plans & Elevations4.7.4Plans & Elevations - Practice4.7.5Nets4.7.6Nets - Practice4.7.7Volume of 3D Shapes4.7.8Volume of 3D Shapes - Practice4.7.9Volume of a Cuboid4.7.10Volume of a Cylinder4.7.11Volume of a Sphere4.7.12Volume of a Hemisphere4.7.13Volume of a Cone4.7.14Volume of a Pyramid4.7.15Surface Area of a Cuboid4.7.16Surface Area of a Cylinder4.7.17Surface Area of a Sphere/Hemisphere4.7.18Surface Area of a Cone4.7.19Surface Area of Composite Shapes4.7.20Surface Area of Composite Shapes - Practice4.7.21End of Topic Test - Triangles, Area, & 3D Shapes4.7.22End of Topic Test - 3D Shapes
4.8

Vectors

4.8.1Vector Introduction4.8.2Vector Introduction - Practice4.8.3Vectors4.8.4Vectors - Practice4.8.5End of Topic Test - Vectors
5

Probability

5.1

Introduction to Probability

5.1.1Probability5.1.2Probability - Practice5.1.3Probability scale5.1.4Probability Scale - Practice5.1.5Randomness & Fairness5.1.6Randomness & Fairness - Practice5.1.7Sum of Probabilities5.1.8Sum of Probabilities - Practice5.1.9Relative & Expected Frequency5.1.10Relative & Expected Frequency - Practice5.1.11Frequency Tables5.1.12Frequency Tables - Practice5.1.13Use Frequency Trees5.1.14Use Frequency Trees - Practice5.1.15Complete Frequency Trees5.1.16Complete Frequency Trees - Practice5.1.17End of Topic Test - Probability
5.2

Representing Probability

5.2.1Sample Space Diagrams5.2.2Sample Space Diagrams - Practice5.2.3Sets5.2.4Sets - Practice5.2.5Venn Diagrams5.2.6Venn Diagrams - Practice5.2.7End of Topic Test - Representing Probability
5.3

Probability Calculations

5.3.1Theoretical Probability5.3.2Theoretical Probability - Practice5.3.3Venn Diagram Probabilities5.3.4Venn Diagram Probabilities - Practice5.3.5Multiple Events5.3.6Multiple Events - Practice5.3.7Dependent & Independent Events5.3.8Dependent & Independent Events - Practice5.3.9Calculating Probabilities5.3.10Calculating Probabilities - Practice5.3.11Complex Tree Diagrams5.3.12Complex Tree Diagrams - Practice5.3.13End of Topic Test - Probability
6

Statistics

6.1

Introduction to Statistics

6.1.1Statistics Basics6.1.2Statistics Basics - Practice6.1.3Statistics Basics 26.1.4Statistics Basics 2 - Practice6.1.5Comparing Data6.1.6Comparing Data - Practice6.1.7Comparing Datasets6.1.8Comparing Datasets - Practice6.1.9Writing Comparisons6.1.10Writing Comparisons - Practice6.1.11Frequency Table6.1.12Frequency Table - Practice6.1.13End of Topic Test - Statistics
6.2

Charts & Graphs

6.2.1Bar Charts6.2.2Bar Charts - Practice6.2.3Pie Charts6.2.4Pie Charts - Practice6.2.5Pictograms6.2.6Pictograms - Practice6.2.7Scatter Graphs6.2.8Scatter Graphs - Practice6.2.9Making Predictions6.2.10Making Predictions - Practice6.2.11Correlation and Causation6.2.12Correlation and Causation - Practice6.2.13Outliers6.2.14Outliers - Practice6.2.15End of Topic Test - Statistics

Practice questions on Congruent Triangles

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What rule makes these triangles congruent?Multiple choice
  2. 2
    What rule makes these triangles congruent?Multiple choice
  3. 3
    What rule makes these triangles congruent?Multiple choice
  4. 4
    What rule makes these triangles congruent?Multiple choice
  5. 5
    Which of these are rules for congruence in triangles?True / false
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Congruence - Practice

Congruent Triangles - Practice