Question

Learning Task 1
Given, AART = AHOP. If mR = 54 and m T = 73. HO = 15cm, AT = 10cm
1. illustrate the two triangles.
2. What angles of AHOP has a measure of 53° and a measure of 54"?
3. Identify the sides with measures equal to HO and AT.
4. If RT= 20cm, find the value of xif OP= 11x-13
5. Which is the shortest side of AART?​

Answer 1

Answer:

The shortest side of $ART$ is $RT.$

Step-by-step explanation:

$\begin{aligned}&O H=15 \mathrm{~cm} \quad A T=10 \mathrm{~cm} \\&\angle A=53^{\circ}\end{aligned}$

$\triangle A R T \cong \triangle H O P$

all sides and angles are equal

$\text { } \begin{aligned}\angle H &=\angle A=53^{\circ} \\\angle O &=\angle R=54^{\circ}\end{aligned}$

$\begin{aligned}&O H=R A=15 \mathrm{~cm} \\&A T=H P=10 \mathrm{~cm}\end{aligned} \quad R T=20 \mathrm{~cm} \quad O P=11 \eta-13 \begin{gathered}11 x-13=20 \\11x=33\end{gathered}$

Answer 2

Answer:

Step-by-step explanation:

Given,

ΔART ≅ ΔHOP

∠R = 54, ∠T = 73, HO = 15cm, AT = 10cm

Recall the concepts

Two triangles are congruent if all the three sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.

The sum of three angles of a triangle is equal to 180.

(1) We have ΔART ≅ ΔHOP,

Since the two triangles, ART and HOP are congruent triangles,

Then by corresponding sides of congruent triangles,

∠A = ∠H, ∠R = ∠O, ∠T = ∠P ---------------------(1)

AT = HP, AR = HO, RT = OP ----------------------(2)

(2) Since the sum of three angles of a triangle is 180, we have,

∠A+∠R+∠T = 180

∠A+54+73 = 180

∠A+127 = 180

∠A = 53

Since ∠A = ∠H, we have ∠H = 53

∠R = ∠O, we have ∠O =54

∴The angles of triangle HOP has a measure 53° and 54° are ∠H and ∠O

(3) By corresponding sides of congruent triangles we have

AT = HP, AR = HO

∴The sides with measures equal to HO and AT are AR and HP

(4) From equation (2) we have, RT = OP

Since RT = 20cm and OP = 11x -13

11x - 13 = 20

11x = 20+13 = 33

x = 3

The value of x = 3

(5)AT = 10cm, HO = AR = 15cm and RT = 20cm

The shortest side is AT

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