15 questions · timed · auto-graded
Two right triangles are congruent if hypoenuse and a side of the other trianlge.
Explenation:
According to RHS congruence criterion the given statment is true.
The two alitutde corresponding to two equal sides of a triangle need not be equal.
Explenation:
Since two sides are equal, the triangle is an isosceles triangle. The two altitudes corresponding to two equal side must be equal.
The bisectors of two equal angles of a triangle are equal.
Explenation:
Since it an isosceles triangle, the lenghts of bisectors of the two equal angles are equal.If the bisector of the verical angle of a triangle bisects the base, then the triangle may be isosceles.
Explenation:
The angular bisector of the vertex angle is also a mediam.
⇒ The tirnagle must be a isosceles and also may be an equilateral triangle.
If any two sides of a right triangle are respectively equal to two sides of other right triangle then the two triangle are congruent.
Explenation:
The two right triangles may or may not be congrunt.
Given
$\triangle\text{ABC},$ extend BA to D such that AD = AC.Now in
$\triangle\text{DBC},$$\angle\text{ADC} = \angle\text{ACD } $ [Angles opposite to equal sides are equal]
Hence
$\angle\text{BCD} > \angle\text{BDC}$That is BD > BC [The side opposite to the larger (greater) angle is longer]
⇒ AB + AD > BC
$\therefore$ AB + AC > BC [Since AD = AC)
Thus sum of two sides of a triangle is always greater than third side.
The measure of each angle of an equilateral triangle 60º.
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Angles opposite to equal sides of a triangle are equal.