Question Please help me answer these questions? Transcribed Image Text: Topic 4: Congruent Triangles 18. Write three valid congruency statements glven the triangles below. View the full answer Step 2/3 Step 3/3 Final answer Transcribed image text: 1. They are congruent by the following three congruen. If three sides are a, b and c, then three conditions should be met.1st step All steps Final answer Step 1/3 The two given triangles P T W and H G W are congruent. ![]() ![]() Approach: A triangle is valid if sum of its two sides is greater than the third side. Examples: Input : a = 7, b = 10, c = 5 Output : Valid Input : a = 1 b = 10 c = 12 Output : Invalid. a) b) c) Tour: Giving the congruency statement, list all congruent…Given three sides, check whether triangle is valid or not. Write three valid congruency statements specify to triangular below. In the diagrams below, if AC = QP, angle A = angle Q, and angle B = angle. The AAS rule states that: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent. In terms of the sides a, b, c, inradius r and circumradius R, : p.Angle-side-angle is a rule used to prove whether a given set of triangles are congruent. ( p + q ) 2 = r 2 + s 2 p 2 + 2 p q + q 2 = p 2 + h 2 ⏞ + h 2 + q 2 ⏞ 2 p q = 2 h 2 ∴ h = p q Using Pythagoras' theorem on the 3 triangles of sides ( p + q, r, s ), ( r, p, h ) and ( s, h, q ), The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hypotenuse is split into. It is common to mark the altitude with the letter h (as in height), often subscripted with the name of the side the altitude is drawn to. Also the altitude having the incongruent side as its base will be the angle bisector of the vertex angle. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. The altitudes are also related to the sides of the triangle through the trigonometric functions. Thus, the longest altitude is perpendicular to the shortest side of the triangle. It is a special case of orthogonal projection.Īltitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length equals the triangle's area. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex. ![]() The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. ![]() The intersection of the extended base and the altitude is called the foot of the altitude. This line containing the opposite side is called the extended base of the altitude. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex. The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. The altitudes from each of the acute angles of an obtuse triangle lie entirely outside the triangle, as does the orthocenter H. For the orthocentric system, see Orthocentric system. "Orthocenter" and "Orthocentre" redirect here.
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