Prove that Two right triangles are congruent if the
hypotenuse and one side of one triangle are respectively equal to the
hypotenuse and one side of the other triangle.
Text Solution
Verified by Experts
In `/_\ABC` and `/_\DEF`,
Hypotenuse is equal in both the two right triangles.
`AC=DF`
One side of the triangle is equal to the other side of the triangle. Let us assume that the two sides are equal.
`AB=DE`
The two triangles are right angled so both the triangles have 90 degree in common.
` /_ABC=/_DEF`
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.6|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.7|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 7.4|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.
Side Side Side(SSS) Congruence : Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.
Show that in a right angled triangle, the hypotenuse is the longest side.
Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.
If two angles and a side of one triangles are equal to two angles and a side of another triangles , the triangles are congruent.
The hypotenuse of a right triangle is 6 m more than the twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.
Find the area of the right-angled triangle with hypotenuse 40 cm and one of the other two sides 24 cm.
Draw a right triangle with hypotenuse of length 5\ c m and one side of length 4\ c mdot
Find the area of a right triangle with hypotenuse of 10 and side of 8
In two right triangles, one side and an acute angle of one triangle are equal to one side and the corresponding acute angle of the other triangle. Prove that the two triangles are congruent.
